Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
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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