## NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.4

#### Page No 315:

#### Question 1:

#### Answer:

Let

*x*^{3}=*t*
∴ 3

*x*^{2}*dx*=*dt*#### Question 2:

#### Answer:

Let 2

*x*=*t*
∴ 2

*dx*=*dt*#### Question 3:

#### Answer:

Let 2 −

*x*=*t*
⇒ −

*dx*=*dt*#### Question 4:

#### Answer:

Let 5

*x*=*t*
∴ 5

*dx*=*dt*#### Question 5:

#### Answer:

#### Question 6:

#### Answer:

Let

*x*^{3}=*t*
∴ 3

*x*^{2}*dx*=*dt*#### Question 7:

#### Answer:

From (1), we obtain

#### Question 8:

#### Answer:

Let

*x*^{3}=*t*
⇒ 3

*x*^{2}*dx*=*dt*#### Question 9:

#### Answer:

Let tan

*x*=*t*
∴ sec

^{2}*x**dx*=*dt*#### Page No 316:

#### Question 10:

#### Answer:

#### Question 11:

19×2+6x+5

#### Answer:

∫19×2+6x+5dx=∫13x+12+22dx

Let (3x+1)=t

∴

3 dx=dt

⇒∫13x+12+22dx=13∫1t2+22dt

=13×2tan-1t2+C

=16tan-13x+12+C

#### Question 12:

#### Answer:

#### Question 13:

#### Answer:

#### Question 14:

#### Answer:

#### Question 15:

#### Answer:

#### Question 16:

#### Answer:

Equating the coefficients of

*x*and constant term on both sides, we obtain
4

*A*= 4 ⇒*A*= 1*A*+

*B*= 1 ⇒

*B*= 0

Let 2

*x*^{2}+*x*− 3 =*t*
∴ (4

*x*+ 1)*dx*=*dt*#### Question 17:

#### Answer:

Equating the coefficients of

*x*and constant term on both sides, we obtain
From (1), we obtain

From equation (2), we obtain

#### Question 18:

#### Answer:

Equating the coefficient of

*x*and constant term on both sides, we obtain
Substituting equations (2) and (3) in equation (1), we obtain

#### Question 19:

#### Answer:

Equating the coefficients of

*x*and constant term, we obtain
2

*A*= 6 ⇒*A*= 3
−9

*A*+*B*= 7 ⇒*B*= 34
∴ 6

*x*+ 7 = 3 (2*x*− 9) + 34
Substituting equations (2) and (3) in (1), we obtain

#### Question 20:

#### Answer:

Equating the coefficients of

*x*and constant term on both sides, we obtain
Using equations (2) and (3) in (1), we obtain

#### Question 21:

#### Answer:

Let

*x*^{2}+ 2*x*+3 =*t*
⇒ (2

*x*+ 2)*dx*=*dt*
Using equations (2) and (3) in (1), we obtain

#### Question 22:

#### Answer:

Equating the coefficients of

*x*and constant term on both sides, we obtain
Substituting (2) and (3) in (1), we obtain

#### Question 23:

#### Answer:

Equating the coefficients of

*x*and constant term, we obtain
Using equations (2) and (3) in (1), we obtain

#### Question 24:

equals

**A.**

*x*tan

^{−1}(

*x*+ 1) + C

**B.**tan

^{− 1}(

*x*+ 1) + C

**C.**(

*x*+ 1) tan

^{−1}

*x*+ C

**D.**tan

^{−1}

*x*+ C

#### Answer:

Hence, the correct answer is B.

#### Question 25:

equals

**A.**

**B.**

**C.**

**D.**

#### Answer:

Hence, the correct answer is B.

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