# Thread: double integral substitution

1. ## double integral substitution

Hi

I am looking at an example in my text and don't understand how they get from step A to step B
Evaluate double integral y sin (xy) dy dx - x is 0 to 1 and y is 0 to pi

let u = y so du = dy
let dv = sin (xy) dy so v = -cos(xy)/x

so here is where I get lost
integral (0 to pi) y sin (xy) dy = -ycos(xy)/x for y= 0 to y=pi +
1/x (integral 0 to pi cos(xy)) dy

I understand the first part but it is the second part that I don't know where it is coming from. Why is it 1/x integral cos (xy) dy?

Thanks in advance for any insight you can provide.

2. Ironically I figured it out looking at someone else question. At the bottom of their post was the formula integral v dv = uv - integral vdu so it all makes sense now.

Thanks to everyone who viewed my post.