The value of int_{-pi/4}^{pi/4} sin^{103} x c | vedclass

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Question

(D) Let $f(x) = \sin^{103} x \cdot \cos^{101} x$. We check if the function is even or odd by evaluating $f(-x)$: $f(-x) = \sin^{103}(-x) \cdot \cos^{1

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(D) Let $f(x) = \sin^{103} x \cdot \cos^{101} x$. We check if the function is even or odd by evaluating $f(-x)$: $f(-x) = \sin^{103}(-x) \cdot \cos^{101}(-x)$ Since $\sin(-x) = -\sin x$ and $\cos(-x) = \cos x$,we have: $f(-x) = (-\sin x)^{103} \cdot (\cos x)^{101} = -\sin^{103} x \cdot \cos^{101} x = -f(x)$. 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,$\int_{-\pi/4}^{\pi/4} \sin^{103} x \cdot \cos^{101} x \, dx = 0$.

The value of $\int_{-\pi/4}^{\pi/4} \sin^{103} x \cdot \cos^{101} x \, dx$ is

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