The value of `int_0^(pi//2)cosx\ e^(sin x)dx\ i s` `1` b. `e-1` c. `0` d. `-1`

Explanation

`e-1`


Let `I=int_{0}^{frac{pi}{2}} cos x e^{sin x} d x`

Let `sin x=t,` then `cos x d x=d t`

When `x=0, t=0` and `x=frac{pi}{2}, t=1`

Therefore the integral becomes


`I=int_{0}^{1} e^{t} d t `

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