The value of int_{-3}^3 sin ^7 x cos ^{16} x | vedclass

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(C) Let $f(x) = \sin^7 x \cos^{16} x$. We check if the function is even or odd by evaluating $f(-x)$. $f(-x) = \sin^7(-x) \cos^{16}(-x)$. Since $\sin(

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(C) Let $f(x) = \sin^7 x \cos^{16} x$. We check if the function is even or odd by evaluating $f(-x)$. $f(-x) = \sin^7(-x) \cos^{16}(-x)$. Since $\sin(-x) = -\sin x$ and $\cos(-x) = \cos x$,we have: $f(-x) = (-\sin x)^7 (\cos x)^{16} = -\sin^7 x \cos^{16} x = -f(x)$. 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,$\int_{-3}^3 \sin^7 x \cos^{16} x \,dx = 0$.

The value of $\int_{-3}^3 \sin ^7 x \cos ^{16} x \,dx$ is

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