AP EAMCET · Maths · Definite Integration
\[
\int_0^x \frac{x}{\sin x}\left(3 \cos ^2 x+2 \sin x+\sin ^3 x-3\right) d x=
\]
- A \(\frac{\pi(5 \pi-12)}{4}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{2}(5 \pi-6)\)
- D \(\frac{\pi(5 \pi-12)}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi(5 \pi-12)}{4}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { given } \int_0^\pi \frac{x}{\sin x}\left(3 \cos ^2 x+2 \sin x+\sin ^3 x-3\right) d x \\ & \Rightarrow \int_0^\pi \frac{x}{\sin x}\left(-3 \sin ^2 x+2 \sin x+\sin ^3 x\right) d x \\ & \Rightarrow \int_0^\pi x\left(\sin ^2 x-3 \sin x+2\right) d…
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