int_{-1}^{1} x^{17} cos^{4} x , dx = | vedclass

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(C) Let $f(x) = x^{17} \cos^{4} x$. We check if the function is even or odd by evaluating $f(-x)$: $f(-x) = (-x)^{17} \cos^{4}(-x) = -x^{17} \cos^{4}

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(C) Let $f(x) = x^{17} \cos^{4} x$. We check if the function is even or odd by evaluating $f(-x)$: $f(-x) = (-x)^{17} \cos^{4}(-x) = -x^{17} \cos^{4} x = -f(x)$. Since $f(-x) = -f(x)$,the function $f(x)$ 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,$\int_{-1}^{1} x^{17} \cos^{4} x \, dx = 0$.

$\int_{-1}^{1} x^{17} \cos^{4} x \, dx = $

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