MHT CET · Maths · Definite Integration
\(\int_{0}^{\frac{\pi}{2}} \sin ^{2} x \mathrm{~d} x=\)
- A \(\frac{\pi}{2}\)
- B \(\frac{3 \pi}{2}\)
- C \(\frac{3 \pi}{4}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\int_{0}^{\frac{\pi}{2}} \sin ^{2} x d x=\frac{1}{2} \int_{0}^{\frac{\pi}{2}}(1-\cos 2 x) d x=\) \(\frac{1}{2}\left[x-\frac{\sin 2 x}{2}\right]_{0}^{\frac{\pi}{2}}\)
\(=\frac{1}{2}\left[\frac{\pi}{2}+0\right]=\frac{\pi}{4} \)
\(=\frac{1}{2}\left[\frac{\pi}{2}+0\right]=\frac{\pi}{4} \)
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