AP EAMCET · Maths · Definite Integration
\(\int_0^{2 \pi} \sin ^6 x \cos ^5 x d x\) is equal to
- A \(2 \pi\)
- B \(\pi / 2\)
- C \(0\)
- D \(-\pi\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
Let \(\begin{aligned} I & =\int_0^{2 \pi} \sin ^6 x \cos ^5 x d x \\ I & =2 \int_0^\pi \sin ^6 x \cos ^5 x d x\end{aligned}\) \([\because f(2 \pi-x)=f(x)]\) Let \(f(x)=\sin ^6 x \cos ^5 x\) \([\because f(\pi-x)=-f(x)]\)…
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