Question

How do you evaluate the definite integral `int sinxdx` from `[0, pi/2]`?

Answer 1

`1`

Explanation:

`int_0^(pi/2)sinxdx`

now `d/(dx)(cosx)=-sinx`

so `intsinxdx=-cosxdx`

`:.int_0^(pi/2)sinxdx=[-cos]_0^(pi/2)`

`=-[cos]_0^(pi/2)=-{cancel((cos(pi/2)))^(=0)-cos0)}`

`=- - 1=1`