Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
The correct evaluation of $\int_0^{\pi / 2} \sin x \sin 2 x d x$ is
A
$\frac{4}{3}$
B
$\frac{1}{3}$
C
$\frac{3}{4}$
✓
$\frac{2}{3}$
✓
Answer
Correct option: D.
$\frac{2}{3}$
(D) Let $I =\int_0^{\pi / 2} \sin x \sin 2 x \ d x=2 \int_0^{\pi / 2} \sin ^2 x \ \cos x \ d x$ Put $\sin x= t \Rightarrow \cos x \ d x= dt$ When $x=0, t =0$ and when $x=\frac{\pi}{2}, t =1$ $\therefore I=2 \int_0^1 t^2 d t=\frac{2}{3}\left[t^3\right]_0^1=\frac{2}{3}$
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