COMEDK · Maths · 30. Definite Integration
\(\int_{-\pi / 2}^{\pi / 2} \sin ^2 x d x\) is equal to
- A 0
- B \(\pi\)
- C \(\frac{\pi}{2}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=\sin ^2 x\) Now, \(\begin{aligned} f(-x) & =\sin ^2(-x)=(\sin (-x))^2 \\ & =(-\sin x)^2=\sin ^2 x=f(x) \end{aligned}\) So, \(f\) is an even function…
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