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

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## 7. Integrals

#### Exercise 7.3

Exersice 7.3

Find the integrals of the following functions in Exercises 1 to 9.

Ques.1.

Ans.

Ques.2.

Ans.   =

Ques.3.

Ans.

Ques.4.

Ans.

Ques.5.

Ans.

Ques.6.

Ans.

Ques.7.

Ans.

Ques.8.

Ans.

Ques.9.

Ans.

Find the integrals of the following functions in Exercises 10 to 18.

Ques.10.

Ans.

Ques.11.

Ans.

Ques12.

Ans.

Ques.13.

Ans.

Ques.14.

Ans. Let I

…..(i)

Putting

From eq. (i), I =

Ques.15.

Ans. Let I

Putting

From eq. (i),

I =

Ques.16.

Ans.

……….(i)

Putting

From eq. (i),

Ques.17.

Ans.

Ques.18.

Ans.

Integrate the following functions in Exercises 19 to 22.

Ques.19.

Ans. Let I ……….(i)

Here  is a negative even integer.

Therefore, multiplying both numerator and denominator by

I =

……….(ii)

Putting

From eq. (ii),

I =

Ques.20.

Ans. Let I

……….(i)

Putting

From eq. (i),

I =

Ques.21.

Ans.

Ques.22.

Ans. Let I  ……….(i)

Multiplying and dividing by  as ,

I =

Choose the correct answer in Exercise 23 and 24.

Ques.23.  is equal to:

(A)

(B)

(C)

(D)

Ans.

hance, option (A) is correct.

Ques.24.  is equal to:

(A)

(B)

(C)

(D)

Ans. Let I =  ……….(i)

Putting

From eq. (i),

I =

hance, option (B) is correct.

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

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