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NCERT solution class 12 chapter 1 Integrals exercise 1.2 mathematics part 2

EXERCISE 1.2


Page No 304:

Question 1:

Answer:

Let t

∴2x dx = dt

Question 2:

Answer:

Let log |x| = t

∴ 

Question 3:

Answer:

Let 1 + log t

∴ 

Question 4:

sin x ⋅ sin (cos x)

Answer:

sin x ⋅ sin (cos x)

Let cos x = t

∴ −sin x dx = dt

Question 5:

Answer:

Let 

∴ 2adx = dt

Question 6:

Answer:

Let ax + b = t

⇒ adx = dt

Question 7:

Answer:

Let 

∴ dx = dt

Question 8:

Answer:

Let 1 + 2x2 = t

∴ 4xdx = dt

Question 9:

Answer:

Let 

∴ (2x + 1)dx = dt

Question 10:

Answer:

Let 

Question 11:

Answer:

Let I=∫xx+4 dxput x+4=t⇒dx=dtNow, I=∫t-4tdt=∫t-4t-1/2dt=23t3/2-42t1/2+C=23.t.t1/2-8t1/2+C=23x+4x+4-8x+4+C=23xx+4+83x+4-8x+4+C=23xx+4-163x+4+C=23x+4x-8+C

 

Question 12:

Answer:

Let 

∴ 

Question 13:

Answer:

Let 

∴ 9x2 dx = dt

Question 14:

Answer:

Let log x = t

∴ 

Question 15:

Answer:

Let 

∴ −8x dx = dt

Question 16:

Answer:

Let 

∴ 2dx = dt

Question 17:

Answer:

Let 

∴ 2xdx = dt

Page No 305:

Question 18:

Answer:

Let 

∴ 

Question 19:

Answer:

Dividing numerator and denominator by ex, we obtain

Let 

∴ 

Question 20:

Answer:

Let 

∴ 

Question 21:

Answer:

Let 2x − 3 = t

∴ 2dx = dt

⇒∫tan22x-3dx = ∫sec22x-3 – 1dx=∫sec2t- 1dt2= 12∫sec2t dt – ∫1dt= 12tant – t + C= 12tan2x-3 – 2x-3 + C

Question 22:

Answer:

Let 7 − 4x = t

∴ −4dx = dt

Question 23:

Answer:

Let 

∴ 

Question 24:

Answer:

Let 

∴ 

Question 25:

Answer:

Let 

∴ 

Question 26:

Answer:

Let 

∴ 

Question 27:

Answer:

Let sin 2x = t

∴ 

Question 28:

Answer:

Let 

∴ cos x dx = dt

Question 29:

cot x log sin x

Answer:

Let log sin x = t

Question 30:

Answer:

Let 1 + cos x = t

∴ −sin x dx = dt

Question 31:

Answer:

Let 1 + cos x = t

∴ −sin x dx = dt

Question 32:

Answer:

Let sin x + cos x = t ⇒ (cos x − sin xdx = dt

Question 33:

Answer:

Put cos x − sin x = t ⇒ (−sin x − cos xdx = dt

Question 34:

Answer:

Question 35:

Answer:

Let 1 + log x = t

∴ 

Question 36:

Answer:

Let 

∴ 

Question 37:

Answer:

Let x4 = t

∴ 4x3 dx = dt

Let 

From (1), we obtain

Question 38:

equals

Answer:

Let 

∴ 

Hence, the correct answer is D.

Question 39:

equals

A. 

B. 

C. 

D. 

Answer:

Hence, the correct answer is B.


 

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