The value of _0^ e ^ ^2 x ^5 3 x d x is - Vidyadip

MCQ

The value of $\int_0^\pi e ^{\cos ^2 x} \cos ^5 3 x d x$ is

A
1
B
-1
✓
$0$
D
$\frac{\pi}{2}$

✓

Answer

Correct option: C.

$0$

(C)
Let $I =\int_0^\pi e ^{\cos ^2 x} \cos ^5 3 x d x$
$=\int_0^\pi e ^{\cos ^2(\pi-x)} \cos ^5 3(\pi-x) d x$
$\ldots\left[\because \int_0^{ a } f (x) d x=\int_0^{ a } f ( a -x) d x\right]$
$\therefore \quad I =-\int_0^\pi e ^{\cos ^2 x} \cos ^5 3 x d x=- I$
$\Rightarrow 2 I =0 \Rightarrow I =0$

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