The value of int_{-1}^1 sin^5 x cos^4 x , dx | vedclass

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(D) Let $f(x) = \sin^5 x \cos^4 x$. We check if the function is even or odd by evaluating $f(-x)$. $f(-x) = \sin^5(-x) \cos^4(-x) = (-\sin x)^5 (\cos

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(D) Let $f(x) = \sin^5 x \cos^4 x$. We check if the function is even or odd by evaluating $f(-x)$. $f(-x) = \sin^5(-x) \cos^4(-x) = (-\sin x)^5 (\cos x)^4 = -\sin^5 x \cos^4 x = -f(x)$. 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,$\int_{-1}^1 \sin^5 x \cos^4 x \, dx = 0$.

The value of $\int_{-1}^1 \sin^5 x \cos^4 x \, dx$ is

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