int_{-1}^{1} sin^{11} x , dx is equal to | vedclass

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(D) Let $f(x) = \sin^{11} x$. To check if the function is even or odd,we evaluate $f(-x)$: $f(-x) = \sin^{11}(-x) = (\sin(-x))^{11} = (-\sin x)^{11} =

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(D) Let $f(x) = \sin^{11} x$. To check if the function is even or odd,we evaluate $f(-x)$: $f(-x) = \sin^{11}(-x) = (\sin(-x))^{11} = (-\sin x)^{11} = -\sin^{11} x = -f(x)$. Since $f(-x) = -f(x)$,the function $f(x) = \sin^{11} x$ is an odd function. According to the property of definite integrals,if $f(x)$ is an odd function,then $\int_{-a}^{a} f(x) \, dx = 0$. Therefore,$\int_{-1}^{1} \sin^{11} x \, dx = 0$.

$\int_{-1}^{1} \sin^{11} x \, dx$ is equal to

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