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Math Help - Integration

  1. #1
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    Integration

    Hey. Please help.

    I have a differentiable function, f

    Find  \int xf '(x^2) \, dx
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by WWTL@WHL View Post
    Hey. Please help.

    I have a differentiable function, f

    Find  \int xf '(x^2) \, dx
    Substitute t=x^2

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  3. #3
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    Thanks for the quick reply, Moo.

    I'm probably being really silly, but I just can't finish it off.

    Using t = x^2

    \int \frac{t^{-\frac{1}{2}}}{2} f '(t) \, dt


    Using substitution by parts...


    \int \frac{t^{-\frac{1}{2}}}{2} f '(t) \, dt = \frac{t^{-\frac{1}{2}}}{2} f'(t) + \frac{1}{4} \int t^{-\frac{3}{2}} f(t)

    Any idea?

    Thanks.

    EDIT: Hang on for 5 mins, I think I've spotted my mistake.
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  4. #4
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    Ok, so my previous post was garbage.

    I've got to:

     \frac{1}{2} \int f'(t) \, dt

     = \frac{1}{2} f(t)

     = \frac{1}{2} f(x^2)

    is this right?
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  5. #5
    Moo
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    Quote Originally Posted by WWTL@WHL View Post
    Ok, so my previous post was garbage.

    I've got to:

     \frac{1}{2} \int f'(t) \, dt

     = \frac{1}{2} f(t)

     = \frac{1}{2} f(x^2)

    is this right?


    Except that you forgot the integration constant !
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  6. #6
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    Constant, Schmanstant

    Excellent. Thanks for your help, Moo.
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