AP EAMCET · Maths · Definite Integration
\(\int_{-\pi}^{\frac{\pi}{2}} \sin x \cdot \sin ^2(\cos x) d x=\)
- A \(\frac{1-\sin 2}{4}\)
- B \(-\left(\frac{1+\sin 2}{4}\right)\)
- C \(\frac{\sin 2-2}{4}\)
- D \(-\left(\frac{2+\sin 2}{4}\right)\)
Answer & Solution
Correct Answer
(C) \(\frac{\sin 2-2}{4}\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-\pi}^{\frac{\pi}{2}} \sin x \cdot \sin ^2(\cos x) d x\) Let \(\cos x=t \Rightarrow-\sin x d x=d t\)…
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