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Thread: Integral

  1. #1
    Dec 2008

    Question Integral

    I need help finding the Integer of x * (x-2)^7.
    I don't understand why I can't figure it out my self because it doesn't seem that difficult. It is for finding the area under the graph between 0 and 2, i keep finding a different answer than that to my calculator gives me. I welcome any help anybody can give me.
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  2. #2
    Junior Member
    Nov 2008
    That integral has a little trick: the difficulty is that you have $\displaystyle (x-2)^7$, which might be difficult to integrate, so do this:
    Perform the change of variables $\displaystyle u=x-2$ and you will transform your integral into $\displaystyle \int_{-2}^{0} (u+2)u^7 du = \int_{-2}^{0} u^8+2u^7 du$ which is much more workable...

    (Im assuming that you wanted to get the integral between 0 and 2).
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