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Math Help - Integration of (x-1)^99

  1. #1
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    Integration of (x-1)^99

    Hi there,

    (x-1)^99 ∂x


    Also, cos^3 () sin () ∂

    t*e^-t^2 ∂t

    many thanks

    Bryn
    Last edited by Bryn; November 27th 2009 at 05:53 AM.
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  2. #2
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    Quote Originally Posted by Bryn View Post
    Hi there,

    (x-1)^99


    many thanks

    Bryn
    \int (x-1)^{99} \, dx = \frac{(x-1)^{100}}{100} + C
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  3. #3
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    But why is this, why doesn't the x-1 need integrating or differentiating

    I can't see how you can just integrate x-1 as if it was q for example

    Thanks
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  4. #4
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    Quote Originally Posted by Bryn View Post
    But why is this, why doesn't the x-1 need integrating or differentiating

    I can't see how you can just integrate x-1 as if it was q for example

    Thanks
    because (x-1) is a function

    q is ?
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  5. #5
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    Quote Originally Posted by skeeter View Post
    \int (x-1)^{99} \, dx = \frac{(x-1)^{100}}{100} + C
    let u=x-1, then du=dx

    and \int (x-1)^{99} \, dx =\int (u)^{99} \, du =\frac{u^{100}}{100} + C= \frac{(x-1)^{100}}{100} + C
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  6. #6
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    Hello Bryn
    Quote Originally Posted by Bryn View Post
    Hi there,

    (x-1)^99 ∂x


    Also, cos^3 () sin () ∂

    t*e^-t^2 ∂t

    many thanks

    Bryn
    All these integrals can be solved by substitution. The first has already been done. I'll start you off for numbers 2 & 3.

    2) Put \cos\phi = u

    Then -\sin\phi\; d\phi=du

    So \int\cos^3\phi\sin\phi\;d\phi = -\int u^3\;du=...

    3) Put e^{-t^2}=u

    Then e^{-t^2}(-2t)\;dt=du

    So ...?

    Grandad
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