A) \[\frac{4}{3}\]
B) \[\frac{1}{3}\]
C) \[\frac{3}{4}\]
D) \[\frac{2}{3}\]
Correct Answer: D
Solution :
Let \[I=\int_{0}^{\pi /2}{\sin x\sin 2x\,dx}=2\int_{0}^{\pi /2}{{{\sin }^{2}}x\cos xdx}\] Put \[t=\sin x\Rightarrow dt=\cos x\,dx\] Now, \[I=2\int_{0}^{1}{{{t}^{2}}dt=\frac{2}{3}[{{t}^{3}}]_{0}^{1}=\frac{2}{3}}\].You need to login to perform this action.
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