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Question: The value of \(\int_{0}^{\pi/2}\frac{2^{\sin x}}{2^{\sin x} + 2^{\cos x}}\) dx is –...

The value of ∫0π/22sin⁡x2sin⁡x+2cos⁡x\int_{0}^{\pi/2}\frac{2^{\sin x}}{2^{\sin x} + 2^{\cos x}} dx is –

A

2

B

p

C

p/4

D

2p

Answer

p/4

Explanation

Solution

I = ∫0π/22sin⁡x/2sin⁡x+2cos⁡xdx\int_{0}^{\pi/2}{2^{\sin x}/2^{\sin x} + 2^{\cos x}}dx ...(1)

By prop. I=dx..(2) (1)&(2)I= p/4