Q110 / 160 · WBJEE 2011 · Mathematics

The value of \(\int_0^\pi \sin ^{50} x \cos ^{49} x d x\) is

  • Correct answer
    A
    0
  • B
    \(\pi / 4\)
  • C
    \(\pi / 2\)
  • D
    1

Solution

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

Hence, the correct answer is option: 'A'.

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