TS EAMCET · Maths · Definite Integration
\(\int_0^\pi x f(\sin x) d x\) is equal to
- A \(2 \pi \int_0^{\frac{\pi}{4}} f(\sin x) d x\)
- B \(\pi \int_0^{\frac{\pi}{4}} f(\sin x) d\)
- C \(2 \pi \int_0^{\frac{\pi}{2}} f(\sin x) d x\)
- D \(\pi \int_0^{\frac{\pi}{2}} f(\sin x) d x\)
Answer & Solution
Correct Answer
(D) \(\pi \int_0^{\frac{\pi}{2}} f(\sin x) d x\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Let } I=\int_0^\pi x f(\sin x) d x \\ & \Rightarrow \quad I=\int_0^\pi(\pi-x) f[\sin (\pi-x)] d x\end{aligned}\)…
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