Question

How do you evaluate the definite integral `int 1+sinx` from `[pi/4, pi/2]`?

Answer 1

`pi/4+sqrt2/2`

Explanation:

`int_(pi/4)^(pi/2)(1+sinx)dx`

`=[x-cosx]_(pi/4)^(pi/2)`

`=[x-cosx]^(pi/2)-[x-cosx]_(pi/4)`

`(pi/2-cos(pi/2))-(pi/4-cos(pi/4))`

`=pi/2-0-pi/4+sqrt2/2`

`pi/4+sqrt2/2`