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  • Need Solution for R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 40 Maths Textbook Solution.

Need Solution for R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 40 Maths Textbook Solution.

Answers (1)

Answer:

\frac{2(\sin x)^{\frac{3}{2}}}{3}-\frac{2}{7}(\sin x)^{\frac{7}{2}}+c

Given:

\int \sqrt{\sin x} \cos ^{3} x d x

Hint:

To solve this equation we have to suppose sin x in term of t and cos x into 2t.

Solution: 

I=\int \sqrt{\sin x} \cos ^{3} x d x                                \left[\because \sqrt{\sin x}=t, \sin x=t^{2}, \cos x d x=2 t d t\right.

    I=\int \sqrt{\sin x}\left(1-\sin ^{2} x\right) \cos x d x

    I=\int t\left(1-t^{4}\right) 2 t d t

    I=\int 2 t^{2} d t-\int 2 t^{6} d t

    I=\frac{2 t^{3}}{3}-\frac{2 t^{7}}{7}+c

    I=\frac{2(\sin x)^{\frac{3}{2}}}{3}-\frac{2}{7}(\sin x)^{\frac{7}{2}}+c

 

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infoexpert21

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