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  • Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise Revision Exercise question 54

Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise Revision Exercise question 54

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Answer:  \frac{\pi^{2}}{8}

Hint: In this equation, we use \int x^{n}dx formula

Given:   \int_{0}^{\frac{\pi}{2}} \frac{x}{\sin ^{2} x+\cos ^{2} x} d x

Solution:

I=\int_{0}^{\frac{\pi}{2}} \frac{x}{\sin ^{2} x+\cos ^{2} x} d x

I=\int_{0}^{\frac{\pi}{2}} x d x                                          \left[\int x^{n} d x=\frac{x^{n+1}}{n+1}+c\right]

\begin{aligned} &I=\left[\frac{x^{2}}{2}\right]_{0}^{\frac{\pi}{2}} \\ & \end{aligned}

I=\frac{\pi^{2}}{8}-0 \\

I=\frac{\pi^{2}}{8}

 

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