AP EAMCET · Maths · Definite Integration
\(\int_0^1 x \operatorname{Sin}^{-1} x d x=\)
- A \(\frac{\pi}{8}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{12}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{8}\)
Step-by-step Solution
Detailed explanation
\( \int_0^1 x \operatorname{Sin}^{-1} x d x = \left[ \frac{x^2}{2} \operatorname{Sin}^{-1} x \right]_0^1 - \int_0^1 \frac{x^2}{2} \frac{1}{\sqrt{1-x^2}} d x \) \( = \left( \frac{1}{2} \operatorname{Sin}^{-1} 1 - 0 \right) - \frac{1}{2} \int_0^1 \frac{x^2}{\sqrt{1-x^2}} d x \)…
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