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  • Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 23

Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Multiple choice question 23

Answers (1)

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Answer:

0

Given:

\int_{-\pi}^{\pi} \sin ^{3} x \cos ^{2} x \; d x

Hint:

This equation is solve by \int_{-a}^{a} f(x) d x
 

Explanation:  

\begin{aligned} &\int_{-a}^{a} f(x) d x \\\\ &f(-x)=\sin ^{3}(-x) \cdot \cos ^{2}(-x) \end{aligned}

\begin{aligned} &=-(\sin x)^{3} \cdot \cos ^{2} x \\\\ &=-\sin ^{3} x \cdot \cos ^{2} x \\\\ &=-f(x) \end{aligned}

f(x) is odd function.

\int_{-\pi}^{\pi} \sin ^{3} x \cos ^{2} x \; d x=0

 

 

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infoexpert26

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