_ ,0 ^ , e^ ^2 x ^3 x ,dx is equals to - Vidyadip

MCQ

$\int_{\,0}^{\,\pi } {{e^{{{\sin }^2}x}}{{\cos }^3}x\,dx} $ is equals to

A
$ - 1$
✓
$0$
C
$1$
D
$\pi $

✓

Answer

Correct option: B.

$0$

b
(b) $I = \int_0^\pi {{e^{{{\sin }^2}x}}{{\cos }^3}x\,\,dx} $

$ \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}x\,dx} $ ..$(ii)$

Adding $(i)$ and $(ii),$ we get

$2I = 0$ ==> $I = 0$.

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