Definite Integration Question 64
Question: $ \int _{0}^{\pi }{{e^{{{\sin }^{2}}x}}{{\cos }^{3}}xdx} $ is equals to
[MP PET 2002]
Options:
A) $ -1 $
B) 0
C) 1
D) $ \pi $
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int_0^{\pi }{{e^{{{\sin }^{2}}x}}{{\cos }^{3}}xdx} $
$ \Rightarrow I=\int_0^{\pi }{{e^{{{\sin }^{2}}(\pi -x)}}{{\cos }^{3}}(\pi -x)}dx $ ……(i)
$ \Rightarrow I=-\int_0^{\pi }{{e^{{{\sin }^{2}}x}}{{\cos }^{3}}xdx} $ …..(ii)
Adding (i) and (ii), we get $ 2I=0 $
therefore $ I=0 $ .
BETA
