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Question: Answered & Verified by Expert
The value of \(\int_0^\pi \sin ^{50} x \cos ^{49} x d x\) is
MathematicsDefinite IntegrationWBJEEWBJEE 2011
Options:
  • A 0
  • B \(\pi / 4\)
  • C \(\pi / 2\)
  • D 1
Solution:
2709 Upvotes Verified Answer
The correct answer is: 0
Hints: \(I=\int_0^\pi \sin ^{50} x \cdot \cos ^{49} x d x \int_0^4 f(x)=\int_0^4 f(a-x)\)
\(\begin{aligned}
& I=\int_0^\pi \sin ^{50} x\left(-\cos ^{49}(x)\right)=-\int_0^\pi \sin ^{50} x \cdot \cos ^{49} x \\
& =I=-I \\
& I=0
\end{aligned}\)

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