NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.11

Exams Prep Master

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.11 is covered in this article. This exercise of Chapter 7 is based on some properties of the definite integral. NCERT Solutions for Class 12 Maths Chapter 7 will carry a weightage of around 6-18 marks in the CBSE Term 2 Exam 2022. NCERT has provided a total of 21 problems and solutions based on the important topics of the exercise.

Download PDF NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.11

NCERT Solutions for Class 12 Maths Chapter 7: Important Topics

Important topics covered in Integrals Chapter are:

Double Integral
Continuous Integration
Properties of Definite Integral
Line Integral
Integrals of Particular Function

Also check: NCERT Solutions for Class 12 Maths Chapter 7 Integrals

CBSE CLASS XII Related Questions

1.
The motion of a particle is described as \( S = 2t^{3} - 6t^{2} + 8 \). Its velocity \( \frac{dS}{dt} \), when the acceleration \( \frac{d^{2}S}{dt^{2}} \) vanishes is :
- \( -6 \) unit/sec
- \( 0 \) unit/sec
- \( 18 \) unit/sec
- \( 6 \) unit/sec
View Solution
2.
For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :
Minimize \(Z = 18x + 10y\)
subject to constraints
\[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]
View Solution
3.
Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).
View Solution
4.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).
View Solution
5.
Evaluate :
\[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]
View Solution
6.
Solve the differential equation \( (x+y)\,dy + (x-y)\,dx = 0 \), given that \( y(1) = 1 \).
View Solution

View All

Similar Mathematics Concepts

Integrals: Types, Formulas, and Properties

Differentiation and Integration Formula: Rules and Applications

Integration: Inverse Process of Differentiation

Integral Calculus: Formula, Types, Methods & Examples

Line Integral: Vector Field and Applications

Integral Formulas: List of Formulas & Methods of Integration

Reduction Formula in Integration: Types and Solved Example

NCERT Solutions For Class 12 Mathematics Chapter 7 Integrals

Integral Calculus Formula: Integration and Terms

Integral Test: Convergence, Divergence, Proof & Conditions

CBSE CLASS XII Previous Year Papers

Mathematics

Mathematics Preparation Guides

Matrices: Types, Properties, Formulas & Examples

Relations and Functions: Explanation, Types, and Representation

Types of Matrices: Row, Column, Zero, Symmetric, Skew Symmetric

Minors and Cofactors of Determinant: Definition, Formula and Solved Examples

Operations on Matrices: Addition, Subtraction, Multiplication and Solved Examples

Determinants: Types, Properties & Examples

Types of Relations: Definition, Classification and Examples

Properties of Determinants: Explanation, Important Properties and Examples

Plane: Equation of a Plane in Three-Dimensional Space

Invertible Matrices: Theorems, Properties and Examples

Symmetric and Skew Symmetric Matrices: Definition and Properties

Types of Functions: Elements, Equations, Range, and Domain

Introduction to Three-Dimensional Geometry: Distance, Important Formulae

Angle between Two Lines: Formula, Derivation & Calculation

Binary Operations: Types, Properties and Examples

Addition of Vectors: Definition, Formula, Laws and Properties

Types of Vectors: Definition, Properties & Examples

Definite Integral: Formula, Properties, Application & Examples

Integration by Partial Fractions: Formula, Steps & Examples

Angle Between a Line and a Plane: Formulas and Solved Examples

Mathematics NCERT Solutions

NCERT Solutions For Class 12 Mathematics Chapter 13: Probability

NCERT Solutions For Class 12 Mathematics Chapter 9: Differential Equations

NCERT Solutions For Class 12 Mathematics Chapter 7 Integrals

NCERT Solutions For Class 12 Mathematics Chapter 12: Linear Programming

NCERT Solutions for Class 12 Maths Chapter 3 Matrices

NCERT Solutions For Class 12 Mathematics Chapter 6 Applications of Derivatives

NCERT Solutions For Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

You can also check

Exercise 7.1 Solutions	22 Questions
Exercise 7.2 Solutions	39 Questions
Exercise 7.3 Solutions	24 Questions
Exercise 7.4 Solutions	25 Questions
Exercise 7.5 Solutions	23 Questions
Exercise 7.6 Solutions	24 Questions
Exercise 7.7 Solutions	11 Questions
Exercise 7.8 Solutions	6 Questions
Exercise 7.9 Solutions	22 Questions
Exercise 7.10 Solutions	10 Questions
Exercise 7.11 Solutions	21 Questions
Miscellaneous Exercise Solutions	44 Questions

Continuous integration	Properties of Definite Integral	Line Integral
Fundamental Theorem of Calculus	Integration by Partial Fractions	Definite Integral Formula
Calculus Formula	Differentiation and Integration Formula	Substitution Method
Methods of Integration	List of Integral Formulas	Double Integral

Arithmetic	Calculus	Algebra
NCERT Solutions for Class 12 Maths	Maths MCQs	Maths Syllabus
Mathematics Notes	Trigonometry	Maths Study Material

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.11

NCERT Solutions for Class 12 Maths Chapter 7: Important Topics

Other Exercises Solutions of Class 12 Maths Chapter 7 Integrals

CBSE CLASS XII Related Questions

1.
The motion of a particle is described as \( S = 2t^{3} - 6t^{2} + 8 \). Its velocity \( \frac{dS}{dt} \), when the acceleration \( \frac{d^{2}S}{dt^{2}} \) vanishes is :

2.
For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :
Minimize \(Z = 18x + 10y\)
subject to constraints
\[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]

3.
Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).

4.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

5.
Evaluate :
\[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

6.
Solve the differential equation \( (x+y)\,dy + (x-y)\,dx = 0 \), given that \( y(1) = 1 \).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.11

NCERT Solutions for Class 12 Maths Chapter 7: Important Topics

Other Exercises Solutions of Class 12 Maths Chapter 7 Integrals

CBSE CLASS XII Related Questions

1.The motion of a particle is described as \( S = 2t^{3} - 6t^{2} + 8 \). Its velocity \( \frac{dS}{dt} \), when the acceleration \( \frac{d^{2}S}{dt^{2}} \) vanishes is :

2.For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :Minimize \(Z = 18x + 10y\)subject to constraints\[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]

3.Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).

4.Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

5.Evaluate :\[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

6.Solve the differential equation \( (x+y)\,dy + (x-y)\,dx = 0 \), given that \( y(1) = 1 \).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The motion of a particle is described as \( S = 2t^{3} - 6t^{2} + 8 \). Its velocity \( \frac{dS}{dt} \), when the acceleration \( \frac{d^{2}S}{dt^{2}} \) vanishes is :

2.
For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :
Minimize \(Z = 18x + 10y\)
subject to constraints
\[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]

3.
Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).

4.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

5.
Evaluate :
\[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

6.
Solve the differential equation \( (x+y)\,dy + (x-y)\,dx = 0 \), given that \( y(1) = 1 \).