1.

`int_(0)^(pi//2) cosx e^(sinx) dx` is equal toA. `e+1`B. `e-1`C. `e`D. `-e`

Answer» Correct Answer - A
Let ` I = int_(0)^(pi//2)cosxe^(sinx)dx`
Put `sinx = t rArr cosx dx = dt`
As `x rarr 0` then `t rarr 0`
and `x rarr pi//2`, then `t rarr 1`
`:. I = int_(0)^(t)e^(t)dt = [e^(t)]_(0)^(1)`
`= e^(1) - e^(0)=e-1`


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