# NCERT Solutions for Exercise 7.9 Class 12 Maths Chapter 7 - Integrals

In NCERT solutions for Class 12 Maths chapter 7 exercise 7.9 is one of the most important exercises from the exam perspective as it deals with the evaluation of definite integrals in a defined range. Such NCERT book questions are more often seen in the Board as well as competitive examination. Solutions to exercise 7.9 Class 12 Maths which are provided here are prepared in detail by the experienced subject matter experts. Considering the importance of NCERT solutions for Class 12 Maths chapter 7 exercise 7.9, it is highly recommended to students to practice at least a few questions before the examination. Also students can refer NCERT chapter Integrals for more practice.

Integrals Exercise 7.1

Integrals Exercise 7.2

Integrals Exercise 7.3

Integrals Exercise 7.4

Integrals Exercise 7.5

Integrals Exercise 7.6

Integrals Exercise 7.7

Integrals Exercise 7.8

Integrals Exercise 7.10

Integrals Exercise 7.11

Integrals Miscellaneous Exercise

**Integrals ****Class 12 ****Chapter 7 Exercise 7.9**

### ** Question:1 ** Evaluate the definite integrals in Exercises 1 to 20.

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:2 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:3 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:4 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:5 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:6 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:7 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:8 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:9 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:10 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:11 ** Evaluate the definite integrals in Exercises 1 to 20.

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:12 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:13 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:14 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

Multiplying by 5 both in numerator and denominator:

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:15 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

Putting which gives,

As, and as .

So, we have now:

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:16 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

So, we can rewrite the integral as;

where . ** ................(1) **

Now, consider

Take numerator

We now equate the coefficients of x and constant term, we get

A=10 and B=-25

Now take denominator

Then we have

Then substituting the value of in equation (1), we get

### ** Question:17 ** Evaluate the definite integrals in Exercises 1 to 20.

### ** Answer: **

Given integral:

Consider the integral

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:18 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

can be rewritten as:

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:19 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

can be rewritten as:

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

or we have

### ** Question:20 ** Evaluate the definite integrals in Exercises 1 to 20.

** **

### ** Answer: **

Given integral:

Consider the integral

can be rewritten as:

So, we have the function of ,

Now, by Second fundamental theorem of calculus, we have

### ** Question:21 ** Choose the correct answer in Exercises 20 and 21.

(A)

(B)

(C)

(D)

### ** Answer: **

Given definite integral

** Consider **

we have then the function of x, as

By applying the second fundamental theorem of calculus, we will get

** Therefore the correct answer is D. **

### ** Question:22 ** Choose the correct answer in Exercises 21 and 22.

equals ** **

** ** (A)

(B)

(C)

(D)

### ** Answer: **

Given definite integral

Consider

Now, putting

we get,

Therefore we have,

we have the function of x , as

So, by applying the second fundamental theorem of calculus, we get

** Therefore the correct answer is C. **

**More About NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.9**

The NCERT Class 12 Maths chapter Integrals is one of the most important chapters of Class 12 Maths NCERT syllabus. If we talk about exercise 7.9 Class 12 Maths, it holds good weightage in the Board examination. NCERT Solutions for Class 12 Maths chapter 7 exercise 7.9 can be learnt easily if practice of some questions is done on a regular basis.

**Also Read| **Integrals Class 12 Notes

**Benefits of NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.9**

The Class 12th Maths chapter 7 exercise is a one stop solution for clearing concepts as well as practicing questions.

Practicing exercise 7.9 Class 12 Maths can be of great help to the students aspiring to score well in the examination.

These Class 12 Maths chapter 7 exercise 7.9 solutions can be asked directly in Board examination which can be verified from looking Previous year questions.

Along with NCERT solutions for Class 12 Maths chapter 7 exercise 7.9 one must also go through the previous year questions of the same topics.

**Also see-**

NCERT Exemplar Solutions Class 12 Maths Chapter 7

NCERT Solutions for Class 12 Maths Chapter 7

**NCERT Solutions Subject Wise**

NCERT Solutions Class 12 Chemistry

NCERT Solutions for Class 12 Physics

NCERT Solutions for Class 12 Biology

NCERT Solutions for Class 12 Mathematics

**Subject Wise NCERT Exemplar Solutions**

NCERT Exemplar Class 12 Maths

NCERT Exemplar Class 12 Physics

NCERT Exemplar Class 12 Chemistry

NCERT Exemplar Class 12 Biology

Happy learning!!!