Definite Integration Question 46
Question: $ \int_0^{\pi }{x}f(\sin x)dx= $
[IIT 1982; Kurukshetra CEE 1993]
Options:
A) $ \pi \int_0^{\pi }{f(\sin x)dx} $
B) $ \frac{\pi }{2}\int_0^{\pi }{f(\sin x)dx} $
C) $ \frac{\pi }{2}\int_0^{\pi /2}{f(\sin x)dx} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \int_0^{\pi }{x}f(\sin x)dx=\frac{\pi }{2}\int_0^{\pi }{f(\sin x)dx} $
Since $ \int_0^{a}{xf(x)dx=\frac{1}{2}a\int_0^{a}{f(x)dx,}} $ if $ f(a-x)=f(x) $ .
BETA
