Get the Class 12 Maths Handwritten Notes PDF below for Class 12 Mathematics Chapter 7 Integrals. The handwritten format makes the Class 12 Maths Handwritten Notes PDF useful as a revision companion to the typed Notes page on the same topic, since each formula appears in a coloured box alongside its derivation.
- CBSE Weightage: 8 to 10 marks (Chapter 7 Integrals plus Chapter 8 Application of Integrals together form the Calculus unit worth roughly 18 marks; expect one 3-marker on substitution or by-parts, one 3-marker on definite-integral properties, and one 5-marker mixing partial fractions or special integrals)
- JEE Main Weightage: 8 to 10% (2 to 3 questions per shift on indefinite integrals, by-parts, partial fractions, and definite-integral properties; among the top three highest-yield Maths chapters)
- JEE Main Weightage: Not in JEE Main syllabus (Maths-only chapter; high weight for JEE Main, JEE Advanced, and CUET Mathematics)
Student Pulse - Integrals Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
The notebook opens with the antiderivative definition and the family of curves picture, locks in the standard-integrals table, then walks through substitution, partial fractions, integration by parts with the ILATE rule, five special integrals, and the six properties of definite integrals, ending with a one-page summary card.
These handwritten notes are prepared by Collegedunia subject mentors, mapped to the 2026-27 NCERT print, and cross-checked against the last five years of CBSE Board and JEE Main papers on Integrals.
Also Check:
- Integrals Class 12 Maths Notes
- Integrals Class 12 Maths NCERT Solutions
- Integrals Class 12 Maths Formula Sheet
Why Integrals Is the Single Highest-Stake Chapter in Class 12 Maths
No other chapter in the 2026-27 NCERT carries the dual scoring power of Integrals. Every CBSE Board paper since 2021 has carried at least one 5-mark question from the Class 12 Maths Handwritten Notes PDF, and JEE Main draws 2 to 3 questions per shift from it. The handwritten notebook is calibrated to that exact pattern.
- Highest CBSE yield per page of NCERT: Integrals delivers roughly 8 to 10 marks for what is effectively three NCERT exercises, the best marks-per-hour ratio in the Class 12 Maths book.
- Pattern-driven, not proof-driven: Almost every question reduces to one of four moves, namely substitution, by-parts via ILATE, partial fractions, or one of the special-integral templates. Memorise the patterns and a 5-mark Integrals question takes under 4 minutes.
- Definite-integral property questions repeat verbatim: The same six properties recycle in CBSE Board papers, and the King-rule property 0a f(x) dx = 0a f(a-x) dx has appeared in every Board paper since 2022.
- JEE Main overlap is total: Apart from definite-integral property questions, every NCERT example in the Class 12 Maths Handwritten Notes PDF maps to a JEE Main shift question from the last five years.
Integrals Video Walkthrough
Source: Magnet Brains on YouTube
How the Class 12 Maths Handwritten Notes PDF on the Class 12 Maths Handwritten Notes PDF Help You
The Class 12 Maths Handwritten Notes PDF address this in the same order as the NCERT textbook.
The 4-page notebook is engineered for two distinct prep modes. The first read internalises the antiderivative idea and the standard-integrals table; subsequent passes focus only on the dashed formula boxes and the last-day card.
- Dashed formula boxes for every standard integral: The 11 most-tested standard formulae sit in their own hand-drawn dashed rectangles, sized so you can scan one page and recall all of them in under 90 seconds.
- ILATE rule card on its own spread: Inverse-trig, Logarithm, Algebraic, Trigonometric, Exponential, written out vertically so the priority order is visual, not memorised as a sentence.
- 2026-27 NCERT alignment: The notebook reflects the current 2026-27 syllabus. NCERT retains the full chapter from antiderivatives through definite-integral properties; the notebook flags every sub-topic CBSE has tested in every Board paper since 2022.
- Solved-pattern templates: One fully solved by-parts example, one substitution example, and one partial-fraction example serve as recipes you can match against any CBSE 5-marker or JEE Main shift question.
Integrals Diagram and Formula-Box Inventory for Class 12 Maths
The Class 12 Maths Handwritten Notes PDF address this in the same order as the NCERT textbook.
The notebook contains 4 conceptual diagrams and 12 dashed formula boxes spread across 4 pages. The table below maps every formula box and figure to its page so a reader hunting one specific concept can jump straight to the right spread.
| Page | Diagram / Box | What It Shows |
|---|---|---|
| 1 | Antiderivative family-of-curves sketch | Three parallel curves y = F(x) + C for different C; visual reason for the "+ C" constant of integration |
| 1 | Standard integrals box (11 entries) | ∫ xn dx, ∫ 1/x dx, ∫ ex dx, ∫ sin x dx, ∫ cos x dx, ∫ sec2 x dx and inverse-trig results, all in one hand-drawn dashed grid |
| 2 | Substitution mechanism panel | t = φ(x), dt = φ'(x) dx ; arrow from messy integral to clean ∫ f(t) dt ; one solved examples ∫ 2x cos(x2) dx |
| 2 | Partial-fraction template box | Three standard forms: A/(x-a), A/(x-a)2, (Ax+B)/(x2+bx+c) ; cover-up rule shorthand |
| 3 | ILATE priority ladder | Vertical ladder I → L → A → T → E with the by-parts formula ∫ u dv = uv - ∫ v du boxed above |
| 3 | Special integrals dashed box | Five hero results: ∫ dx/(x2 ± a2) , ∫ dx/√a2 - x2 , ∫ dx/√x2 ± a2 , each annotated with its trig substitution |
| 4 | Definite integral area sketch | Shaded region under y = f(x) between x = a and x = b ; FTC formula ab f dx = F(b) - F(a) boxed beside |
| 4 | Even / odd property panel | Side-by-side graphs of an even and odd function with the integral collapses = 20a f and = 0 flagged |
Class 12 Maths Integrals Concept-Flavoured Mnemonics
The Class 12 Maths Handwritten Notes PDF address this in the same order as the NCERT textbook.
Four concept mnemonics the notebook repeats on its formula pages. Memorise these and you can recover most MCQ-style facts on this chapter without re-deriving anything.
Integrals Top 8 Standard Results for Class 12 Maths Quick Recall
These eight results cover nearly every Board / JEE Main question on this chapter since 2021. The full learn table with all 70+ formulae and the "when to use which" decision tree lives on the dedicated Formula Sheet.
| Pattern | Result |
|---|---|
| Power Rule | ∫ xn dx = xn+1n+1 + C, n ≠ -1; ∫ 1x dx = log|x| + C |
| Exponential | ∫ ex dx = ex + C; ∫ ax dx = axlog a + C |
| Basic Trig | ∫ sin x dx = -cos x + C; ∫ cos x dx = sin x + C |
| Inverse-Trig Results | ∫ dx√1 - x2 = sin-1 x + C; ∫ dx1 + x2 = tan-1 x + C |
| Special Integral 1 | ∫ dxx2 + a2 = 1atan-1(xa) + C |
| Special Integral 2 | ∫ dxx2 - a2 = 12alog|x - ax + a| + C |
| Integration by Parts | ∫ u dv = uv - ∫ v du ; choose u by ILATE order |
| ex Helper | ∫ ex [f(x) + f'(x)] dx = ex f(x) + C ; the JEE Main shortcut |
Full learn table: Integrals Class 12 Maths Formula Sheet
Integrals: Last 24-Hour Revision Card for Class 12 Maths
The card below is the single page you scan the night before the Board exam. Skip the long derivations; the marks come from the standard-integrals box, the ILATE ladder, the five special integrals, and the six definite-integral properties.
- Antiderivative: ddxF(x) = f(x) ⇒ ∫ f(x) dx = F(x) + C . Always carry the +C in indefinite integrals.
- Standard table (11 results): power, 1/x , ex , ax , sin, cos, sec2, csc2 , sec x tan x , csc x cot x , 1/√1-x2 , 1/(1+x2) .
- Substitution: Set t = φ(x), dt = φ'(x) dx . Pick t to cancel the chain-rule factor; integrate in t; back-substitute.
- Partial fractions: Decompose P(x)/Q(x) (deg P < deg Q) into A/(x-a), A/(x-a)2, (Ax+B)/(x2+bx+c) . Solve for A, B, C; integrate each piece.
- By parts (ILATE): ∫ u dv = uv - ∫ v du . Pick u as earliest in I → L → A → T → E. 5-mark CBSE favourite.
- Special integrals: ∫ dxx2 ± a2, ∫ dx√a2 - x2, ∫ dx√x2 ± a2 . Match the radicand to the right template.
- FTC: ab f(x) dx = F(b) - F(a) where F is any antiderivative of f.
- Six properties: swap limits flips sign; equal limits give 0; split at c; King rule 0a f(x) dx = 0a f(a-x) dx ; even-odd collapse on [-a, a] ; doubling rule on [0, 2a] .
Handwritten Notes vs Printed Notes for Integrals: When to Use Which
The notebook is not a replacement for the typed Notes page. The two resources serve different stages of prep.
| Resource | Best For | Time Per Pass |
|---|---|---|
| Typed Notes | First read, deep concept walk, antiderivative-family proof, FTC derivation | 120 to 150 min |
| Handwritten Notes | Second and third revision passes, formula-box recall, last-24-hour skim | 30 to 45 min |
| Formula Sheet | Final 10 minutes before the paper, standard-table and special-integral recall | 10 min |
The recommended sequence is typed Notes first, then two passes through these handwritten notes, then the Formula Sheet on exam morning.
Related Links:
Class 12th Maths Chapter 7 Integrals Pen-Colour Convention
the Class 12 Maths Handwritten Notes PDF uses four ink colours consistently so you can skim a 4-page notebook in under three minutes during last-day revision.
| Ink Colour | What It Marks | What's Inside |
|---|---|---|
| Blue | Definition / statement | NCERT one-line definitions: antiderivative, indefinite integral, definite integral, FTC, even / odd function |
| Orange | Formula box (dashed) | The 11 standard integrals, the 4 substitution patterns, the 5 special integrals, and the by-parts identity. Each formula has its own hand-drawn dashed rectangle |
| Yellow highlight | MCQ-trap callout | The 6 facts CBSE and JEE re-use as MCQ distractors: forgotten +C, missing absolute-value bars, odd-on-symmetric = 0, ILATE order, King rule, ex(f+f') shortcut |
| Red | Common-mistake box | Common slips: dropped +C, sign error on ∫ sin = -cos , wrong choice of u in by-parts, partial-fraction setup with wrong template |
Integrals Weightage Across Class 12 Maths Chapters
The bar chart below maps the typical CBSE Board mark distribution across the 13 chapters of the 2026-27 NCERT Mathematics book, averaged over the last five years. Chapter 7 Integrals is highlighted in orange and visibly tops the chart.
Integrals tops the bar chart at 9 marks out of the typical 80-mark CBSE paper and pairs with Chapter 8 Application of Integrals for a combined 12 to 14 marks in the Calculus unit, the single highest-yield region of the Class 12 Maths paper.
More Integrals Maths Class 12 Resources
NCERT Handwritten Notes for Class 12 Maths: All Chapters
Use the table below to jump to any other Class 12 Maths chapter's handwritten notebook PDF. The same dashed formula-box convention and last-day revision card runs through every chapter.
| Chapter | Resource |
|---|---|
| Chapter 1 | Relations and Functions Handwritten Notes |
| Chapter 2 | Inverse Trigonometric Functions Handwritten Notes |
| Chapter 3 | Matrices Handwritten Notes |
| Chapter 4 | Determinants Handwritten Notes |
| Chapter 5 | Continuity and Differentiability Handwritten Notes |
| Chapter 6 | Application of Derivatives Handwritten Notes |
| Chapter 8 | Application of Integrals Handwritten Notes |
| Chapter 9 | Differential Equations Handwritten Notes |
| Chapter 10 | Vector Algebra Handwritten Notes |
| Chapter 11 | Three Dimensional Geometry Handwritten Notes |
| Chapter 12 | Linear Programming Handwritten Notes |
| Chapter 13 | Probability Handwritten Notes |
Class 12 Maths Handwritten Notes PDF: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Exercise-wise Breakdown of the Integrals Chapter
The Integrals chapter splits into 10 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked solutions.
| Exercise | Topic Tested |
|---|---|
| Exercise 7.1 | Indefinite integrals; standard formulas |
| Exercise 7.2 | Integration by substitution |
| Exercise 7.3 | Integration using trigonometric identities |
| Exercise 7.4 | Integrals of special functions |
| Exercise 7.5 | Integration by partial fractions |
| Exercise 7.6 | Integration by parts |
| Exercise 7.7 | Integrals of special types |
| Exercise 7.8 | Definite integrals; fundamental theorem of calculus |
| Exercise 7.9 | Evaluation of definite integrals by substitution |
| Exercise 7.10 | Properties of definite integrals |
| Miscellaneous Exercise | Mixed indefinite and definite integration problems |
PDF Download Formats and Languages for the Integrals Chapter
The Integrals Class 12 PDF on this page is available in three formats - each suited to a different revision style. The table below summarises what each format is best for:
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 2-3 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 8-10 MB |
| Handwritten Notes PDF | Mirrors how a topper writes the chapter under Sunday-revision pace | 5-7 MB |
The integrals class 12 ncert pdf and the parallel Hindi-medium edition both follow the same notation and equation numbering as the printed NCERT 2026-27 release. Key points students should know:
- NCERT-faithful: Every definition, theorem and exercise on the integrals class 12 ncert pdf matches the printed textbook line for line.
- Hindi-medium edition: The integrals class 12 pdf is also available in Hindi - same page numbering, same equation labels.
- Formula PDF separate: The integrals class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
- Solutions PDF separate: The integrals class 12 solutions pdf gives every NCERT exercise worked out step by step.
- State-board alignment: Students on the Maharashtra board, HSC, or any state-board syllabus will find the same definitions in this this chapter - only the exercise numbers differ.
Tip: Many toppers keep two parallel copies - a printed formula sheet on A4 for desk revision (the integrals class 12 formulas pdf), and the full these notes on a phone for commute revision. Both files are free and linked above.
Important Questions and Previous Year Trends for the Integrals Chapter
The most repeated question patterns in CBSE Class 12 Maths for the Integrals chapter have settled into a stable cluster across 2019 to 2024 boards. Three question templates account for over 80% of the marks this chapter contributes:
| Template | Typical Marks | What it tests |
|---|---|---|
| Proof / property verification | 3 marks | Students show that a given relation/function/expression satisfies the chapter's definitions. |
| One-step computation | 2 marks | Substitution-based item: plug into a known formula and simplify. |
| Case-study scenario | 4 marks | Real-world setup applying the chapter's definitions, introduced in CBSE 2021+ papers. |
Walking through one example of each template before the exam covers most of the predictable integrals class 12 important questions you will see on board day.
- integrals class 12 previous year questions for 2019-2024 are linked from the PYQ block at the bottom of this page - the exact CBSE phrasings.
- The integrals class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
- For NCERT Exemplar practice, the matching integrals class 12 extra questions set adds advanced problems suitable for JEE Main and JEE Advanced.
- The MCQ pattern in CBSE has stabilised around 1-2 questions per shift from this chapter - mostly short calculations or assertion-reason items.
Year-wise PYQ Distribution
The table below maps the dominant question type asked from the Integrals chapter across recent CBSE Class 12 Maths boards:
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Property verification + case-study item | 5-6 marks |
| 2023 | Computation with proof + assertion-reason MCQ | 5-6 marks |
| 2022 | Long-answer derivation + 2-mark substitution | 5-7 marks |
| 2021 | Definition recall + property check | 4-5 marks |
| 2020 | One-step computation + 3-mark proof | 5 marks |
The full integrals class 12 important questions with solutions set (every year, every paper, every question type) is linked from the PYQ page at the bottom of this article.
How the Integrals Notes Pair with NCERT Solutions and the Formula Sheet
The Integrals Class 12 notes work best when paired with two sister resources from the Class 12 Maths hub. The table below shows how each resource fits into a typical revision week:
| Resource | Use it for | When |
|---|---|---|
| Integrals Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| integrals class 12 ncert solutions PDF | Step-by-step solved exercises | Second pass, during NCERT practice |
| integrals class 12 formulas PDF | One-page identity recall | Third pass, alongside mock papers |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
Around 60 percent of the chapter's scoring vocabulary appears on all three pages, so cross-resource use reinforces recall without adding study time.
- The integrals class 12 ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
- The integrals class 12 solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
- The integrals class 12 formulas reference sheet is the same A4 file students sometimes refer to as integrals class 12 all formulas - it lists every identity used in the chapter.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board integrals class 12 textbook PDF all share the same core definitions.
- For class-first search phrasings - class 12 integrals solutions, class 12 integrals ncert solutions, ncert class 12 integrals solutions - the same files cover the request.
Reference Books and State-Board Mapping
Students using reference books beyond NCERT, or studying under a state board, can map this chapter cleanly:
| Reference | How it maps to Integrals Class 12 |
|---|---|
| RD Sharma Class 12 Integrals | Question patterns overlap with NCERT at ~70%; an advanced supplement. |
| ML Aggarwal Class 12 Integrals | Solutions style is closer to JEE; good for problem-solving practice. |
| Teachoo integrals class 12 | Free online walkthroughs; useful for video-style learning. |
| Shaalaa integrals class 12 solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board integrals class 12 textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| NCERT Exemplar Class 12 Integrals | Advanced problems for JEE Main/JEE Advanced preparation. |
How to Use the Integrals Notes Page Most Effectively
The recommended study plan for the Integrals Class 12 chapter splits across three sittings. The table below outlines what to do in each:
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition and theorem statement. Then read the formula recall section on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in NCERT without looking at the solution first. Compare your steps against the printed working. Use the integrals class 12 ncert solutions PDF if stuck. |
| Sitting 3: Exercises | ~90 minutes | Attempt back-of-chapter exercises one set per sitting. Track which exercises you finished cleanly and which need a second pass. Click into the linked exercise pages above for verification. |
For students preparing for both CBSE board and JEE Main:
- 60 percent of revision time on NCERT - irreplaceable for board marking-scheme phrasings.
- 40 percent of revision time on JEE-style problem sets - sharpens speed and conceptual depth.
- The integrals class 12 important questions set on the previous-year page is the closest free analogue to a JEE-style problem set for this chapter.
- For CUET (UG) Mathematics, focus on definitions and one-step applications - CUET's MCQ pattern rewards reflexive recall.
Class 12 Maths Handwritten Notes PDF - Frequently Asked Questions
Ques. Where can I download the Class 12 Maths Handwritten Notes PDF for free?
Ans. You can download the Integrals Class 12 Maths Handwritten Notes PDF directly from the Class 12 Maths Handwritten Notes PDF. Both the Normal and HD versions are available, and both are free.
Ques. Is this Class 12 Maths Handwritten Notes PDF aligned with the 2026-27 NCERT syllabus?
Ans. Yes. The notebook reflects the current 2026-27 syllabus for Class 12 Mathematics. NCERT retains Chapter 7 Integrals in full, namely antiderivatives, the standard-integrals table, substitution, partial fractions, integration by parts, special integrals, the Fundamental Theorem of Calculus, and the six properties of definite integrals. The handwritten layer flags every sub-topic CBSE has tested in every Board paper since 2022.
Ques. How many pages is the Class 12th Maths Integrals Handwritten Notes PDF?
Ans. The handwritten notes PDF runs 4 pages and covers antiderivatives with a family-of-curves sketch, the 11 standard integrals in a dashed grid, the substitution method with a solved examples, integration by parts with the ILATE priority ladder, partial fractions across three standard templates, five special integrals, the Fundamental Theorem of Calculus with an area-under-curve sketch, and the six properties of definite integrals on a single page, ending with a one-page revision card.
Ques. What is the difference between definite and indefinite integrals?
Ans. An indefinite integral ∫ f(x) dx = F(x) + C returns a family of antiderivatives parameterised by the constant of integration C.
A definite integral ab f(x) dx = F(b) - F(a) returns a single number, the net signed area between the curve y = f(x) , the x-axis, and the vertical lines x = a and x = b .
Page 1 of the notebook draws the antiderivative family; page 4 draws the definite-integral area panel and the Fundamental Theorem of Calculus.
Ques. How do I choose u and dv in integration by parts?
Ans. Use the ILATE rule. The five categories are Inverse-trigonometric, Logarithmic, Algebraic, Trigonometric, and Exponential. Whichever function in your integrand sits earliest in this list becomes u; the rest, including the dx, becomes dv.
So in ∫ x log x dx , Logarithmic beats Algebraic, hence u = log x and dv = x dx . The notebook shows the ILATE ladder as a vertical priority chart on page 3.
Ques. Do these handwritten notes help with JEE Main Integrals questions?
Ans. Yes. JEE Main draws 2 to 3 questions per shift from Integrals, and the yellow MCQ-trap boxes in the notebook is calibrated against the last five years of JEE Main papers.
The covered traps include the odd-function-on-symmetric-interval shortcut, the King-rule property, the ex[f(x) + f'(x)] shortcut, the scaling-rule pitfalls, and partial-fraction setup with the wrong template. Together with the standard-integrals box, these account for the bulk of JEE Main Integrals questions.
Ques. What is the difference between Collegedunia's Handwritten Notes and the regular Notes for Class 12 Maths Chapter 7?
Ans. The regular typed Notes carry the deep concept walk-through with the full antiderivative theory, the Fundamental Theorem of Calculus proof, and every property derivation.
These Handwritten Notes compress the same content into a faster, more visual revision tool with dashed formula boxes, the ILATE ladder, the special-integrals dashed box, and a 24-hour pre-exam recall card. Use the typed Notes for first read, then these for two recall passes.
Ques. Which sub-topic of Integrals carries the most weight in CBSE Board exams?
Ans. The 5-mark Board question almost always comes from one of two places, namely a definite-integral evaluation using the six properties (especially the King rule 0a f(x) dx = 0a f(a-x) dx ) or an indefinite integral that combines partial fractions with one of the five special-integral templates.
Together these two sub-topics account for roughly 5 of the 8 to 10 marks CBSE assigns to this chapter. The notebook places its King-rule callout and partial-fraction template box on exactly these two sub-topics.
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