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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

Answers (1)

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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