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Provide Solution for RD Sharma Class 12 Chapter 19 Definite Integrals Exercise Revision Exercise Question 38

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Answer:  0

Hint: To solve this equation, we have to use f(x) formula

Given:  \int_{0}^{2 \pi} \cos ^{7} x d x 


\begin{aligned} &I=\int_{0}^{2 a} f(x) d x=\int_{0}^{a}[f(x)+f(2a-x)] d x \\ & \end{aligned}

I=\int_{0}^{\frac{\pi}{2}} \cos ^{7} x+\cos ^{7}(2 \pi-x) d x

\begin{aligned} &I=2 \int_{0}^{\frac{\pi}{2}} \cos ^{7} x d x \\ & \end{aligned}


I=2 \int_{0}^{\frac{\pi}{2}}\left(\cos ^{7} x-\cos ^{7} x\right) d x

I= 0

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