Definite Integration Question 339
Question: If $ n $ is any integer, then $ \int_0^{\pi }{{e^{{{\cos }^{2}}x}}{{\cos }^{3}}(2n+1)xdx=} $
[IIT 1985; RPET 1995; UPSEAT 2001]
Options:
A) $ x $
B) 1
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Since $ \cos (2n+1)(\pi -x)=\cos [(2n+1)\pi $
$ -(2n+1)x] $
= $ -\cos (2n+1)x $ and $ {{\cos }^{2}}(\pi -x)={{\cos }^{2}}x $
So that $ f(2a-x)=-f(x) $ , and hence by the property of definite integral $ \int_0^{\pi }{{e^{{{\cos }^{2}}x}}{{\cos }^{3}}(2n+1)xdx=0} $ .
BETA
