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Math Help - integration probem

  1. #1
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    integration probem

    I'm having problems figuring this out...

    why does

    INTa to b [y(x^2y')']dx = INTa to b [(yx^2y')'] - INa to b [x^2(y')^2]dx

    Thank you!

    Note: INTa to b just means "integral fom a to b"
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by romtik View Post
    I'm having problems figuring this out...

    why does

    INTa to b [y(x^2y')']dx = INTa to b [(yx^2y')'] - INa to b [x^2(y')^2]dx

    Thank you!

    Note: INTa to b just means "integral fom a to b"
     \int_{a}^{b} yx^{2y}\,dx = \int_{a}^{b} yx^{2y} \, dx - \int_{a}^{b} x^2y^2 \, dx does not make sense. What do the ' represent?
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by romtik View Post
    I'm having problems figuring this out...

    why does

    INTa to b [y(x^2y')']dx = INTa to b [(yx^2y')'] - INa to b [x^2(y')^2]dx

    Thank you!

    Note: INTa to b just means "integral fom a to b"
    I cant tell but are you trying to do a method of integration by parts where \int_a^{b}y(x^2y')'dx=\int_a^{b}y(x^2\frac{dy^2}{d  ^2x}+2x\frac{dy}{dx})dx?
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