_0^ 2 2008^ x 2008^ x +2008^ x d x= - Vidyadip

MCQ

$\int_0^{\frac{\pi}{2}} \frac{2008^{\sin x}}{2008^{\sin x}+2008^{\cos x}} d x=$

A
$0$
B
$\pi$
✓
$\frac{\pi}{4}$
D
$\frac{\pi}{2}$

✓

Answer

Correct option: C.

$\frac{\pi}{4}$

(C)
Here, $a =2008$
$\int_0^{\frac{\pi}{2}} \frac{ a ^{\sin x}}{ a ^{\sin x}+ a ^{\cos x}} d x=\int_0^{\frac{\pi}{2}} \frac{ a ^{\cos x}}{ a ^{\sin x}+ a ^{\cos x}} d x=\frac{\pi}{4}$
$\therefore \int_0^{\frac{\pi}{2}} \frac{2008^{\sin x}}{2008^{\sin x}+2008^{\cos x}} d x=\frac{\pi}{4}$

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