The value of int_0^{2pi } {{cos }^{99}x,dx} | vedclass

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(D) Let $I = \int_0^{2\pi } {{\cos }^{99}x\,dx}$.Using the property $\int_0^{2a} f(x) dx = 2\int_0^a f(x) dx$ if $f(2a-x) = f(x)$:Since $\cos^{99}(2\p

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(D) Let $I = \int_0^{2\pi } {{\cos }^{99}x\,dx}$.Using the property $\int_0^{2a} f(x) dx = 2\int_0^a f(x) dx$ if $f(2a-x) = f(x)$:Since $\cos^{99}(2\pi - x) = \cos^{99}x$,we have $I = 2\int_0^{\pi} \cos^{99}x\,dx$.Using the property $\int_0^a f(x) dx = 0$ if $f(a-x) = -f(x)$:Since $\cos^{99}(\pi - x) = -\cos^{99}x$,the integral $\int_0^{\pi} \cos^{99}x\,dx = 0$.Therefore,$I = 2 	imes 0 = 0$.

The value of $\int_0^{2\pi } {{\cos }^{99}x\,dx} $ is

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