The NCERT Exemplar Class 12 Maths Integrals PDF provided here include the complete NCERT Exemplar chapter for Class 12 Mathematics Chapter 8 Application of Integrals. The NCERT Exemplar Class 12 Maths Integrals PDF are aligned to the 2026-27 NCERT release and serve as the standard practice set after the main textbook exercises.
- CBSE Weightage: 5-6 marks (typically one 5-mark LA on area between two curves)
- JEE Main Weightage: 2-3% (1 question per shift, almost always a single-correct MCQ)
- JEE Main Weightage: Not applicable (Mathematics is not a JEE Main subject)
The chapter is short on theory: four formulas in section 8.1, then straight to problems. The page below carries the problem-range map, question-type split, Exemplar vs textbook step-up and a parallel-track plan.
This Exemplar PDF is sourced from the official NCERT print and tagged by curve-pair for drilling one family at a time.
Also Check:
- Application of Integrals Class 12 Maths NCERT Exemplar Solutions
- Application of Integrals Class 12 Maths NCERT Book PDF
Why the NCERT Exemplar Matters for Class 12 Maths Application of Integrals
The NCERT Exemplar Class 12 Maths Integrals PDF address this in the same order as the NCERT textbook.
The textbook carries 17 problems plus a short Miscellaneous Exercise. The Exemplar adds 34 more across every curve-pair JEE Main and CBSE recycle.
- Curve-Pair Variety: Parabola-line, parabola-parabola, ellipse, circle-line, modulus and parametric ( x = at2, y = 2at ). The textbook covers fewer than half.
- Sketch-Then-Integrate Habit: Over 70% of Exemplar problems explicitly demand a sketch. CBSE awards 1 mark for it on every 5-mark LA.
- JEE-Pattern MCQs: 11 Exercise MCQs plus 3 Solved-Example MCQs mirror the JEE Main single-correct format.
Application of Integrals NCERT Exemplar Video Walkthrough
Source: Shivang Maths Academy on YouTube
How the NCERT Exemplar Class 12 Maths Integrals PDF on the NCERT Exemplar Class 12 Maths Integrals PDF Help You
The NCERT Exemplar Class 12 Maths Integrals PDF address this in the same order as the NCERT textbook.
The bare Exemplar print is a problem book with almost no scaffolding. This Collegedunia download adds prep aids for the JEE Main and CBSE Board double track.
- Four-Formula Reference Card: The four area formulas in section 8.1, including the split-integral case.
- Curve-Pair Tagging: Each problem tagged by curve pair so you can drill one family at a time.
- Question-Type Tagging: SA, LA or MCQ label on every problem.
- Sketch Hint Annotations: Each LA carries the sketch shape to draw before integrating.
Application of Integrals Exemplar Question-Type Distribution
The NCERT Exemplar Class 12 Maths Integrals PDF address this in the same order as the NCERT textbook.
The 48 problems split across three types. CBSE-prep students prioritise SA and LA; JEE aspirants prioritise MCQs plus Ex 10-12.
| Type | Count | Marks Each | Total Marks | Best For |
|---|---|---|---|---|
| Solved Examples | 14 | - | - | Skill modelling |
| Short Answer (SA) | 15 | 2-4 | ~45 | CBSE SA Section |
| Long Answer (LA) | 8 | 5-6 | ~44 | CBSE 5-mark LA |
| MCQ (Objective Type) | 11 | 1 | 11 | JEE Main + CBSE MCQ |
| Fill-in (Solved Examples) | 2 | - | - | Recall drills |
What's Inside the NCERT Exemplar Class 12 Maths Integrals PDF
Every entry in the NCERT Exemplar Class 12 Maths Integrals PDF is reproduced in the order it appears in the NCERT textbook.
The 9 pages run as one connected problem set with minimal theory. The table below maps each problem range to its type and pages.
| Section | Problem Range | Pages | What It Covers |
|---|---|---|---|
| 8.1 Overview (formulas) | 4 formulas | 1 | Four area formulas plus split-integral case |
| Solved Examples: SA + LA | Ex 1 to Ex 9 | 1-6 | Sine, ay2=x3 , parabola-line, two parabolas, ellipse, cycloid, circle segment |
| Solved Examples: MCQ + Fill-in | Ex 10 to Ex 14 | 6-7 | Area MCQs on circle, ellipse, y=x2 ; recall fill-ins |
| Exercise: Short Answer | Q1 to Q15 | 7-8 | Parabola-line, two-parabolas, cubic-line, semicircle, modulus |
| Exercise: Long Answer | Q16 to Q23 | 8 | Parabola-circle, sine on [0,2π] , triangle, inequality region, modulus |
| Exercise: Objective (MCQ) | Q24 to Q34 | 8-9 | Single-correct MCQs on circle, ellipse, parabola, sine, modulus |
Old vs Current 2026-27 Syllabus Alignment for Chapter 8 Exemplar
The Exemplar was not updated during the 2022-23 revision, but the Chapter 8 textbook itself changed very little, so the Exemplar remains almost fully aligned with the current 2026-27 syllabus.
| Topic | In 2026-27 Textbook? | In Exemplar PDF? | Should You Solve? |
|---|---|---|---|
| Area under y = f(x) | Yes | Yes | Priority 1 |
| Area between two curves | Yes | Yes | Priority 1 |
| Area of ellipse and circle | Yes | Yes | Yes |
| Parametric form (Ex 5, Ex 7) | Trimmed | Yes | Useful for JEE; skip if pure CBSE |
| Region by inequalities (Q19) | Yes | Yes | Yes, esp. for JEE |
Roughly 5% of Exemplar problems use parametric forms the current textbook only shows as solved examples. JEE aspirants should solve them all; board-only students can skip Ex 5 and Q7 if pressed.
Detailed kept-trimmed-removed table: this chapter Maths NCERT Book PDF
How to Use the Exemplar with the NCERT Textbook: 4-Day Parallel-Track Plan
The Exemplar is not a replacement for the NCERT Exemplar Class 12 Maths Integrals PDF. Interleave them: read, then attempt Exemplar problems on the same topic.
- Day 1 (Area Under One Curve): Read Section 8.1 and first half of 8.2; attempt Exemplar SA Q1, Q7, Q9, Q10, Q12 and Solved Examples 1-2.
- Day 2 (Area Between Two Curves): Finish Section 8.2; attempt Exemplar SA Q2-Q6, Q14-Q15 under a 60-minute timer.
- Day 3 (Standard Curves): Revise standard-form integrals; attempt LA Q16, Q19, Q22 plus Ex 4, 8, 9 in 75 minutes.
- Day 4 (Objective Drill): MCQs Q24-Q34 plus Ex 10-12 back to back at 90 seconds per MCQ for JEE Main calibration.
Related Links:
Other Resources
NCERT Exemplar Book PDF for Class 12 Mathematics: All Chapters
Download any other chapter's Exemplar PDF below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 8 | Application of Integrals Exemplar Book PDF |
| Chapter 1 | Relations and Functions NCERT Exemplar Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Exemplar Book PDF |
| Chapter 3 | Matrices NCERT Exemplar Book PDF |
| Chapter 4 | Determinants NCERT Exemplar Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Exemplar Book PDF |
| Chapter 6 | Application of Derivatives NCERT Exemplar Book PDF |
| Chapter 7 | Integrals NCERT Exemplar Book PDF |
| Chapter 9 | Differential Equations NCERT Exemplar Book PDF |
| Chapter 10 | Vector Algebra NCERT Exemplar Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Exemplar Book PDF |
| Chapter 12 | Linear Programming NCERT Exemplar Book PDF |
| Chapter 13 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 12 Maths Integrals PDF: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback - Application of 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.
NCERT Exemplar Class 12 Maths Integrals PDF - Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 12 Maths Integrals PDF for free?
Ans. You can download these notes Maths NCERT Exemplar Book PDF directly from the NCERT Exemplar Class 12 Maths Integrals PDF. Both Normal and HD versions are free.
Ques. How many pages and how many problems are in the Class 12 Maths Application of Integrals Exemplar PDF?
Ans. The Exemplar PDF for Chapter 8 runs 9 pages. It contains 14 solved examples plus 34 unsolved problems split as 15 SA, 8 LA and 11 MCQ (Objective Type).
Ques. Is this NCERT Exemplar Class 12 Maths Integrals PDF aligned with the 2026-27 NCERT syllabus?
Ans. Yes, almost fully. The Exemplar itself was not revised during the 2022-23 update, but the Chapter 8 textbook itself changed very little. Only the parametric-form Solved Examples (Ex 5 and Q7) sit slightly beyond the strict CBSE-only scope; JEE aspirants should still attempt them.
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Application of Integrals?
Ans. Yes. The Exemplar pairs two curves in almost every problem, demands a rough sketch and intersection points before the integral, and uses parametric or implicit forms more often. This is the style that CBSE Boards now use for 5-mark LA on the NCERT Exemplar Class 12 Maths Integrals PDF, and the format JEE Main uses for its single-correct MCQ.
Ques. How important is the NCERT Exemplar for JEE Main preparation on Application of Integrals?
Ans. Very important. JEE Main carries 1 question on Application of Integrals in almost every shift, and the question is calibrated to the Exemplar style: area enclosed by a standard curve pair or a region defined by an inequality. Exemplar Q19 ( y2 ≤ 6ax and x2 + y2 ≤ 16a2 ) is almost identical to a JEE Main 2024 Shift 2 problem.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style for Application of Integrals?
Ans. Long Answer problems Q16 (parabola-circle), Q19 (region inequality) and Q22 (modulus of 2cos x ) most closely match CBSE Board 5-mark style. Solved Examples 6, 8 and 9 are also at exactly this difficulty.
Ques. Should I attempt the Exemplar before or after the NCERT textbook for Chapter 8?
Ans. Attempt them in parallel. Read a topic from the NCERT Exemplar Class 12 Maths Integrals PDF, solve the matching textbook exercise, then attempt Exemplar problems on the same topic. Trying the Exemplar before the NCERT Exemplar Class 12 Maths Integrals PDF usually leaves students stuck on intersection points and sketch construction.
Ques. What is the formula for area enclosed between two curves used across the Exemplar?
Ans. For curves y = f(x) and y = g(x) with f(x) ≥ g(x) on [a, b] , the area is ab [f(x) - g(x)] dx . When the relative position flips at some c ∈ (a, b) , split the integral:
ac [f(x) - g(x)] dx + cb [g(x) - f(x)] dx . The Exemplar section 8.1 lists this as formula 8.1.4 and roughly a third of the LA problems rely on it.
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