Definite Integration Question 494
Question: The value of $ \int_0^{\pi }{{e^{{{\cos }^{2}}x}}{{\cos }^{5}}3x}dx $ is
[Bihar CEE 1994]
Options:
A) 1
B) $ -1 $
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ I=\int_0^{\pi }{{e^{{{\cos }^{2}}x}}{{\cos }^{5}}3xdx=\int_0^{\pi }{{e^{{{\cos }^{2}}x}}{{\cos }^{5}}3(\pi -x)dx}} $ , $ [\because \int_0^{a}{f(x)dx=}\int_0^{a}{f(a-x)dx]} $
$ I=-\int_0^{\pi }{{e^{{{\cos }^{2}}x}}{{\cos }^{5}}3xdx=-I} $
therefore $ 2I=0\Rightarrow I=0 $ .
BETA
