int_{-1}^1 sin ^7 x cdot cos ^6 x , dx = . | vedclass

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(C) Let $f(x) = \sin^7 x \cdot \cos^6 x$. Check if the function is even or odd by evaluating $f(-x)$: $f(-x) = \sin^7(-x) \cdot \cos^6(-x)$ Since $\si

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(C) Let $f(x) = \sin^7 x \cdot \cos^6 x$. Check if the function is even or odd by evaluating $f(-x)$: $f(-x) = \sin^7(-x) \cdot \cos^6(-x)$ Since $\sin(-x) = -\sin x$ and $\cos(-x) = \cos x$,we have: $f(-x) = (-\sin x)^7 \cdot (\cos x)^6 = -\sin^7 x \cdot \cos^6 x = -f(x)$. Since $f(-x) = -f(x)$,the function $f(x)$ is an odd function. According to the property of definite integrals,$\int_{-a}^a f(x) \, dx = 0$ if $f(x)$ is an odd function. Therefore,$\int_{-1}^1 \sin^7 x \cdot \cos^6 x \, dx = 0$.

$\int_{-1}^1 \sin ^7 x \cdot \cos ^6 x \, dx = $ . . . . . . .

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