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NCERT solution class 12 chapter 1 Integrals exercise 1.4 mathematics part 2

EXERCISE 1.4


Page No 315:

Question 1:

Answer:

Let x3 = t

∴ 3x2 dx = dt

Question 2:

Answer:

Let 2x = t

∴ 2dx = dt

Question 3:

Answer:

Let 2 − t

⇒ −dx = dt

Question 4:

Answer:

Let 5x = t

∴ 5dx = dt

Question 5:

Answer:

Question 6:

Answer:

Let x3 = t

∴ 3x2 dx = dt

Question 7:

Answer:

From (1), we obtain

Question 8:

Answer:

Let x3 = t

⇒ 3x2 dx = dt

Question 9:

Answer:

Let tan x = t

∴ sec2x 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

4A = 4 ⇒ A = 1

A + B = 1 ⇒ B = 0

Let 2x2 + x − 3 = t

∴ (4x + 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

2A = 6 ⇒ A = 3

−9A + B = 7 ⇒ B = 34

∴ 6x + 7 = 3 (2x − 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 x2 + 2x +3 = t

⇒ (2x + 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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