## NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.3

#### Page No 307:

#### Question 1:

#### Answer:

#### Question 2:

#### Answer:

It is known that,

#### Question 3:

cos 2

*x*cos 4*x*cos 6*x*#### Answer:

It is known that,

#### Question 4:

sin

^{3}(2*x*+ 1)#### Answer:

Let

#### Question 5:

sin

^{3}*x*cos^{3}*x*#### Answer:

#### Question 6:

sin

*x*sin 2*x*sin 3*x*#### Answer:

It is known that,

#### Question 7:

sin 4

*x*sin 8*x*#### 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:

sin

^{4}*x*#### Answer:

#### Question 11:

cos

^{4}2*x*#### Answer:

#### Question 12:

#### Answer:

#### Question 13:

#### Answer:

#### Question 14:

#### Answer:

#### Question 15:

#### Answer:

#### Question 16:

tan

^{4}*x*#### 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 (

*e*

^{x}

*x*) + C

**B.**tan (

*xe*

^{x}) + C

**C.**tan (

*e*

^{x}) + C

**D.**cot (

*e*

^{x}) + C

#### Answer:

Let

*e*^{x}*x*=*t*
Hence, the correct answer is B.

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