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Math Help - Integral Area

  1. #1
    Newbie
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    Integral Area

    Hello fellow math members!

    I can't find this area of this two function intersecion:
    Y1= x^3-x
    Y2=sin(pi*x)

    For -1\leq x\leq 1

    From what I know, I need to do y1=y2 initially, right?
    But even that I did't get to resolve =/

    Any help? ^^

    Here is the answer:
    Spoiler:
    Area=(8+pi)/pi



    Thanks!
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  2. #2
    Senior Member MacstersUndead's Avatar
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    Re: Integral Area

    A graphical representation of the intersections of the two functions would be sufficient in my opinion, but if you want to be slightly more rigorous:

    When x = -1, 0, 1 then both x^3-x = x(x-1)(x+1) and sin([pi x) = 0
    In the interval (-1,0), sin([pi x) > 0 and x^3-x < 0 so the two functions cannot be equal.
    In the interval (0,1), "" < 0 and "" > 0 so the two functions cannot be equal.

    Hence the only intersection points are -1, 0, 1. then set up your integrals.

    one will be from -1 to 0 with sin(pi x) - (x^3-x) and the other will be from 0 to 1 with (x^3-x) - sin(pi x). After solving both, add them to get your total area.
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  3. #3
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    Re: Integral Area

    Thanks a lot mate!
    Just did it!
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