Definite Integration Question 313
Question: The correct evaluation of $ \int_0^{\pi /2}{\sin x\sin 2x} $ is
[MP PET 1993, 2003]
Options:
A) $ \frac{4}{3} $
B) $ \frac{1}{3} $
C) $ \frac{3}{4} $
D) $ \frac{2}{3} $
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ I=\int_0^{\pi /2}{\sin x\sin 2xdx}=2\int_0^{\pi /2}{{{\sin }^{2}}x\cos xdx} $
Put $ t=\sin x\Rightarrow dt=\cos xdx $
Now, $ I=2\int_0^{1}{t^{2}dt=\frac{2}{3}[t^{3}]_0^{1}=\frac{2}{3}} $ .
BETA
