Evaluate int_{-1}^{1} sin^{5} x cos^{4} x , d | vedclass

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

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(A) Let $I = \int_{-1}^{1} \sin^{5} x \cos^{4} x \, dx$. Define $f(x) = \sin^{5} x \cos^{4} x$. 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,$I = 0$.

Evaluate $\int_{-1}^{1} \sin^{5} x \cos^{4} x \, dx$

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