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Math Help - double integral substitution

  1. #1
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    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.
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  2. #2
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    Feb 2009
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    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.
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