Definite Integration Question 25
Question: $ \int_0^{\pi }{{{\sin }^{2}}xdx} $ is equal to
[MP PET 1999]
Options:
A) $ \pi $
B) $ \frac{\pi }{2} $
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int_0^{\pi }{{{\sin }^{2}}xdx=2\int_0^{\pi /2}{{{\sin }^{2}}xdx}} $ ,
$ \because \int_0^{2a}{f(x)=2\int_0^{a}{f(a-x)dx}} $ , if $ f(2a-x)=f(x) $
$ I=2\times \frac{1}{2}\times \frac{\pi }{2}=\frac{\pi }{2} $ .
BETA
