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NCERT solution class 12 chapter 1 Integrals exercise 1.3 mathematics part 2

EXERCISE 1.3


Page No 307:

Question 1:

Answer:

Question 2:

Answer:

It is known that, 

Question 3:

cos 2x cos 4x cos 6x

Answer:

It is known that,

Question 4:

sin3 (2x + 1)

Answer:

Let 

Question 5:

sin3 x cos3 x

Answer:

Question 6:

sin x sin 2x sin 3x

Answer:

It is known that, 

Question 7:

sin 4x sin 8x

Answer:

It is known that,

sin A . sin B = 12cosA-B-cosA+B∴∫sin4x sin8x dx=∫12cos4x-8x-cos4x+8xdx=12∫cos-4x-cos12xdx=12∫cos4x-cos12xdx=12sin4x4-sin12x12+C

Question 8:

Answer:

Question 9:

Answer:

Question 10:

sin4 x

Answer:

Question 11:

cos4 2x

Answer:

Question 12:

Answer:

Question 13:

Answer:

Question 14:

Answer:

Question 15:

Answer:

Question 16:

tan4x

Answer:

From equation (1), we obtain

Question 17:

Answer:

Question 18:

Answer:

Question 19:

Answer:

1sinxcos3x=sin2x+cos2xsinxcos3x=sinxcos3x+1sinxcosx

 

⇒1sinxcos3x=tanxsec2x+1cos2xsinxcosxcos2x=tanxsec2x+sec2xtanx

Question 20:

Answer:

Question 21:

sin−1 (cos x)

Answer:

It is known that,

Substituting in equation (1), we obtain

Question 22:

Answer:

Question 23:

 is equal to

A. tan x + cot x + C

B. tan x + cosec x + C

C. − tan x + cot x + C

D. tan x + sec x + C

Answer:

Hence, the correct answer is A.

Question 24:

 equals

A. âˆ’ cot (exx) + C

B. tan (xex) + C

C. tan (ex) + C

D. cot (ex) + C

Answer:

Let exx = t

Hence, the correct answer is B.

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