WBJEE · Maths · Definite Integration
The value of \(\int_0^\pi \sin ^{50} x \cos ^{49} x d x\) is
- A 0
- B \(\pi / 4\)
- C \(\pi / 2\)
- D 1
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
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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