Question

Question #f09cc

Answer 1

`-cospix+c`

Explanation:

`int pisinpix`

We bring out the constant `pi` outside the integral

`piintsinpix`

Now we can apply U-Substitution

`Let` `u=pix`

`piintsinu` `dx`

`(du)/dx=pi`

We want to get `du` by itself so we multiply both sides by `dx`.

`du=pi` `dx`

`color(blue)piintsinu` `color(blue)dx`

Since we have `color(blue)pi` `color(blue)dx` in the integral we can substitute it for `du`.

`intsinu` `du`

Now since everything is in terms of `du` you can integrate:

`intsinu` `du` `rArr` `-cosu+c`

Substitute `u` into the answer:

`-cospix+c`