Question

How do you evaluate the definite integral `int e^cosx*sinx` from `[0,pi/4]`?

Answer 1

`= e - e^(1/sqrt 2)`

Explanation:

`int_0^(pi/4) e^cosx*sinx \ dx`

`= int_0^(pi/4) d/dx (color(red)(-) e^cosx) \ dx`

`= [- e^cosx]_0^(pi/4)`

`= e - e^(1/sqrt 2)`