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Thread: Area between the curves

  1. #1
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    Area between the curves

    I am asked to find the area between the two curves below with respect to [0,1].

    y = (((x^2)((x^3)+1)^10)/11)+3

    and

    y = (-((x)((x^2)+1)^10)/11)+3

    I am having a lot of difficulty finding the integral.

    Thanks

    Alex
    Last edited by alex.caine; Apr 19th 2010 at 09:41 AM.
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  2. #2
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    Having you drawn the picture?
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  3. #3
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    Yes I drew it and plugged it into my calculator and it looks like a number that is not countable. I made a mistake with my formulas though in the above post that i will correct.
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  4. #4
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    The formula for integrating the area between two curves is

    \int_{a}^{b}[f(x)-g(x)]dx

    Where f(x) is the top curve and g(x) is the bottom curve.

    or
    \int_{a}^{b}\int_{g_1(x)}^{g_2(x)}f(x,y)dydx
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  5. #5
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    Okay, that I know

    Then you end up with an integral that I do not know how to solve which is my problem...

    You get the integral of

    (((x^2)(x^3+1)^10)/11)+(((x)(x^2+1)^10)/11)

    This is where I am stuck.. Finding the answer to the above integral.
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  6. #6
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    If you can't combine them, break them up into two separate integrals and add the results of both integrals.
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  7. #7
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    Quote Originally Posted by alex.caine View Post
    Okay, that I know

    Then you end up with an integral that I do not know how to solve which is my problem...

    You get the integral of

    (((x^2)(x^3+1)^10)/11)+(((x)(x^2+1)^10)/11)

    This is where I am stuck.. Finding the answer to the above integral.

    Nevermind.
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  8. #8
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    Then, once you have two integrals, use u-sub to simplify your integrals
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  9. #9
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    Could you please inform me what u-sub is
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  10. #10
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    substitution
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  11. #11
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    I do not know the formula for that...
    If anyone other than dsmith could be of assistance it would be greatly appreciated
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