# NCERT Solutions for Exercise 7.3 Class 12 Maths Chapter 7 - Integrals

NCERT solutions for Class 12 Maths chapter 7 exercise 7.3 is another exercise of the NCERT syllabus chapter integrals. It exposes students to some higher level of problems of integrals which includes complex trigonometric functions. Exercise 7.3 Class 12 Maths can be directly solved by students here only to understand the concepts well. NCERT Solutions for Class 12 Maths chapter 7 exercise 7.3 provided below are holistic in nature and have been prepared by experienced faculties. NCERT solutions for exercise 7.3 Class 12 Maths chapter 7 cannot be neglected to perform better in exams like JEE Main. Students can have a look at the NCERT chapter exercises below.

Integrals Exercise 7.1

Integrals Exercise 7.2

Integrals Exercise 7.4

Integrals Exercise 7.5

Integrals Exercise 7.6

Integrals Exercise 7.7

Integrals Exercise 7.8

Integrals Exercise 7.9

Integrals Exercise 7.10

Integrals Exercise 7.11

Integrals Miscellaneous Exercise

**Integrals ****Class 12 ****Chapter 7** Exercise: 7.3

** Question:1 ** Find the integrals of the functions

### ** Answer: **

using the trigonometric identity

we can write the given question as

=

### ** Question:2 ** Find the integrals of the functions

### ** Answer: **

Using identity

, therefore the given integral can be written as

### ** Question:3 ** Find the integrals of the functions

### ** Answer: **

Using identity

Again use the same identity mentioned in the first line

### ** Question:4 ** Find the integrals of the functions

### ** Answer: **

The integral can be written as

Let

Now, replace the value of t, we get;

### ** Question:5 ** Find the integrals of the functions

### ** Answer: **

rewrite the integral as follows

Let

......(replace the value of t as )

### ** Question:6 ** Find the integrals of the functions

### ** Answer: **

Using the formula

we can write the integral as follows

### ** Question:7 ** Find the integrals of the functions

### ** Answer: **

Using identity

we can write the following integral as

=

### ** Question:8 ** Find the integrals of the functions

### ** Answer: **

We know the identities

Using the above relations we can write

### ** Question:9 ** Find the integrals of the functions

### ** Answer: **

The integral is rewritten using trigonometric identities

### ** Question:10 ** Find the integrals of the functions

### ** Answer: **

can be written as follows using trigonometric identities

Therefore,

### ** Question:11 ** Find the integrals of the functions

### ** Answer: **

now using the identity

now using the below two identities

the value

.

the integral of the given function can be written as

### ** Question:12 ** Find the integrals of the functions

### ** Answer: **

Using trigonometric identities we can write the given integral as follows.

### ** Question:13 ** Find the integrals of the functions

### ** Answer: **

We know that,

Using this identity we can rewrite the given integral as

### ** Question:14 ** Find the integrals of the functions

### ** Answer: **

Now,

### ** Question:15 ** Find the integrals of the functions

### ** Answer: **

Therefore integration of =

.....................(i)

Let assume

So, that

Now, the equation (i) becomes,

### ** Question:16 ** Find the integrals of the functions

### ** Answer: **

the given question can be rearranged using trigonometric identities

Therefore, the integration of = ...................(i)

Considering only

let

now the final solution is,

### ** Question:17 ** Find the integrals of the functions

### ** Answer: **

now splitting the terms we can write

Therefore, the integration of

### ** Question:18 ** Find the integrals of the functions

### ** Answer: **

The integral of the above equation is

Thus after evaluation, the value of integral is tanx+ c

### ** Question:19 ** Find the integrals of the functions

### ** Answer: **

Let

We can write 1 =

Then, the equation can be written as

put the value of ** tan = t So, that **

### ** Question:20 ** Find the integrals of the functions

### ** Answer: **

we know that

therefore,

let

Now the given integral can be written as

### ** Question:21 ** Find the integrals of the functions

### ** Answer: **

using the trigonometric identities we can evaluate the following integral as follows

### ** Question:22 ** Find the integrals of the functions

### ** Answer: **

Using the trigonometric identities following integrals can be simplified as follows

### ** Question:23 ** Choose the correct answer

### ** Answer: **

The correct option is (A)

On reducing the above integral becomes

### ** Question:24 ** Choose the correct answer

### ** Answer: **

The correct option is (B)

Let .

So,

(1+ )

therefore,

**More About NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.3**

The NCERT Class 12 Maths chapter Integrals provided here is of good quality and can be referred by students preparing for various examinations. **Exercise 7.3 Class 12 Maths** is important for some of the NCERT book Physics topics also. Hence NCERT Solutions for Class 12 Maths chapter 7 exercise 7.3 are good to go for both Maths as well as Physics.

**Also Read| **Integrals Class 12 Notes

**Benefits of NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.3**

The Class 12th Maths chapter 7 exercise provided here is of best quality.

Students can skip questions from exercise 7.3 Class 12 Maths which are repeated in concept to save their time.

These Class 12 Maths chapter 7 exercise 7.3 solutions are helpful for NEET, JEE as well as Board examinations.

NCERT Solutions for class 12 maths chapter 7 exercise 7.3 are highly recommended to students. Theory also can be understood with the help of exercise solutions only.

**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

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