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# Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Class 12 Maths Important Questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22 are created here for helping the class 12 students in boosting their preparation for class 12 maths exam of CBSE Board term 2 exam 2021-22. These solutions will give an idea of solving the questions on integral accessed in the question paper of CBSE Board term 2 exams 2021-22. Each question is selected from last years class 12 maths question papers keeping in view the format of term 2 class 12 maths question paper  2021-22.

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What is differentiation?

## Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Ans. The given function is

Let t = 3x

dt/dx = 3

dt = 3dx

Substituting 3dx by dt,we have

We know

Substituting t=3x,we have

Ans. The given function is

2x – x² = -[x² -2x +1 -1]= -[(x – 1)² -1] =1 – (x – 1)²

Substituting this value in the function

Ans. The given function is

Q4. Evaluate

9 + 8x – x² =-(x² -8x -9) = -(x² -8x +4² -4²-9)=-[(x -4)² -25] =5² – (x -4)²

Sustituting this value in the denominator

Q5. Evaluate

Ans. Let t = 7 – 4x

differentiating both sides

dt/dx = -4

dt = -4 dx

dx = -dt/4

Substituting this value in the function

Q6. Evaluate

Ans. The given function is

Ans. The given function is

Q8. Evaluate

Ans. The given function is

Q9. If x >a then evaluate

Ans. The given function is

Q10. Evaluate

Ans. The given function is

Let t = √x

t² = x

2t.dt/dx = 1

dx = 2t.dt

Substituting these values ,we get

= 2t + C

Substituting the value t= √x

= 2√x + C

Q11.Evaluate

Ans. Let the given function is f(x)

Therefore given function is an even function

=2(e – 1)

=2e -2

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## NCERT Solutions of  Science and Maths for Class 9,10,11 and 12

### NCERT Solutions of class 9 maths

 Chapter 1- Number System Chapter 9-Areas of parallelogram and triangles Chapter 2-Polynomial Chapter 10-Circles Chapter 3- Coordinate Geometry Chapter 11-Construction Chapter 4- Linear equations in two variables Chapter 12-Heron’s Formula Chapter 5- Introduction to Euclid’s Geometry Chapter 13-Surface Areas and Volumes Chapter 6-Lines and Angles Chapter 14-Statistics Chapter 7-Triangles Chapter 15-Probability Chapter 8- Quadrilateral

### NCERT Solutions of class 9 science

CBSE Class 9-Question paper of science 2020 with solutions

CBSE Class 9-Sample paper of science

CBSE Class 9-Unsolved question paper of science 2019

### NCERT Solutions of class 10 maths

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

### Solutions of class 10 last years Science question papers

CBSE Class 10 – Question paper of science 2020 with solutions

CBSE class 10 -Latest sample paper of science

### NCERT solutions of class 11 maths

 Chapter 1-Sets Chapter 9-Sequences and Series Chapter 2- Relations and functions Chapter 10- Straight Lines Chapter 3- Trigonometry Chapter 11-Conic Sections Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry Chapter 5-Complex numbers Chapter 13- Limits and Derivatives Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning Chapter 7- Permutations and Combinations Chapter 15- Statistics Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

### NCERT solutions of class 12 maths

 Chapter 1-Relations and Functions Chapter 9-Differential Equations Chapter 2-Inverse Trigonometric Functions Chapter 10-Vector Algebra Chapter 3-Matrices Chapter 11 – Three Dimensional Geometry Chapter 4-Determinants Chapter 12-Linear Programming Chapter 5- Continuity and Differentiability Chapter 13-Probability Chapter 6- Application of Derivation CBSE Class 12- Question paper of maths 2021 with solutions Chapter 7- Integrals Chapter 8-Application of Integrals

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