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AP EAMCET · Maths · Definite Integration

\(\int_{-\pi}^{\frac{\pi}{2}} \sin x \cdot \sin ^2(\cos x) d x=\)

  1. A \(\frac{1-\sin 2}{4}\)
  2. B \(-\left(\frac{1+\sin 2}{4}\right)\)
  3. C \(\frac{\sin 2-2}{4}\)
  4. D \(-\left(\frac{2+\sin 2}{4}\right)\)
Verified Solution

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 \(\cos x=t \Rightarrow-\sin x d x=d t\)…