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CBSE And NCERT Solutions:

# NCERT Solutions for Class 12 Mathematics-II english Medium 7. Integrals

Page 6 of 12

## 7. Integrals

#### Exercise 7.6

Exercise 7.6

Integrate the functions in Exercises 1 to 22.

Ques.1.

Ans.

[By product rule]

Ques.2.

Ans.

[By product rule]

Ques.3.

Ans.

[By product rule]

[Again By product rule]

Ques.4.

Ans.

[By product rule]

Ques.5.

Ans.

[By product rule]

Ques.6

Ans.

[BY product rule]

Ques.7.

Ans. Let I =

Putting

I =

[Integrating by parts]

Ques.8.

Ans. Let I =

Ques.9.

Ans. Let I =  ……….(i)

Putting

From eq. (i),

I =

[Applying product rule]

Putting  and

Ques.10.

Ans. Putting

[By product rule]

[Again By product rule]

Ques.11.

Ans. Let I ……….(i)

Putting

From eq. (i),

I =

[By product rule]

Ques.12.

Ans.

[By product rule]

Ques.13.

Ans. Let I

=

Ques.14.

Ans.

=

Ques.15.

Ans.

[By product rule]

Ques.16.

Ans. Let I =

It is in the form of  since,

here  and

I =

Ques.17.

Ans. Let I =

I =

It is in the form of  since,

here  and

I =

Ques.18.

Ans. Let I =

It is in the form of  since,

here  and

### Ques.19.

Ans. Let I =

It is in the form of  since,

here  and

I =

### Ques.20.

Ans. Let I =

I =

It is in the form of  since,

here  and

.

I =

### Ques.21.

Ans. Let I =

[By product rule]

I =

I =

[Again By product rule]

I =

5I =

I =

### Ques.22.

Ans. Putting

=

[By product rule]

### Choose the correct answer in Exercise 23 and 24.

Ques.23.  equals to

(A)

(B)

(C)

(D)

Ans. Let I =

……….(i)

Putting

From eq. (i), I =

hance, option (B) is correct.

### Ques.24.  equals:

(A)

(B)

(C)

(D)

Ans. Let I =

It is in the form of  since,

here  and

I =

hance, option (B) is correct.

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Page 6 of 12

## Topic Lists:

##### NCERT Solutions⇒Class 12th ⇒ Mathematics-II ⇒ Chapter 7. Integrals:

See other sub-topics of this chapter:

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