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  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 36 Maths Textbbok Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise  Revision Exercise Question 36 Maths Textbbok Solution.

Answers (1)

Answer:

\frac{\sin ^{6} x^{2}}{12}+c

Given:

\int x \sin ^{5} x^{2} \cos x^{2} d x

Hint:

To solve this statement we have to suppose or assume sin x and  cos x as v and dv.

Solution: 

I=\int x \sin ^{5} x^{2} \cos x^{2} d x

   I=\frac{1}{2} \int \sin ^{5} t costdt \quad\left[\because x^{2}=t, 2 x d x=d t, x d x=\frac{d t}{2}\right]

I=\frac{1}{2} \int v^{5} d v                                        [\because \sin t=v, \cos t d t=d v]

I=\frac{1}{2} \frac{v^{6}}{6}+c

I=\frac{1}{2} \frac{\left(\sin ^{6} t\right)}{6}+c

I=\frac{\sin ^{6} x^{2}}{12}+c

 

Posted by

infoexpert21

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