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The value of \(\int_0^\pi \sin ^{50} x \cos ^{49} x d x\) is
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Hints: \(I=\int_0^\pi \sin ^{50} x \cdot \cos ^{49} x d x \int_0^4 f(x)=\int_0^4 f(a-x)\)
\(\begin{aligned}
& I=\int_0^\pi \sin ^{50} x\left(-\cos ^{49}(x)\right)=-\int_0^\pi \sin ^{50} x \cdot \cos ^{49} x \\
& =I=-I \\
& I=0
\end{aligned}\)
\(\begin{aligned}
& I=\int_0^\pi \sin ^{50} x\left(-\cos ^{49}(x)\right)=-\int_0^\pi \sin ^{50} x \cdot \cos ^{49} x \\
& =I=-I \\
& I=0
\end{aligned}\)
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