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

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

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best_answer

Answer:  0

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

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

Solution:

\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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