Definite Integration Question 29
Question: $ \int _{-a}^{a}{\sin xf(\cos x)dx=} $
[RPET 1997]
Options:
A) $ 2\int_0^{a}{\sin xf(\cos x)dx} $
B) 0
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int _{-a}^{a}{\sin xf(\cos x)dx} $
$ f(x)=\sin xf(\cos x)\Rightarrow f(-x)=-\sin xf(\cos x) $
$ \because f(x) $ is an odd function
$ \therefore I=\int _{{}}^{{}}{f(x)dx=0} $ .
BETA
