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Math Help - how would i integrate this

  1. #1
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    how would i integrate this

    would i just integrate as normal, the double integral is putting me off.
    could someone show me how id do:

     \int\limits_0^2 \int\limits_{x^{2}-2}^x x^{2} dydx

    thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by skystar View Post
    would i just integrate as normal, the double integral is putting me off.
    could someone show me how id do:

     \int\limits_0^2 \int\limits_{x^{2}-2}^x x^{2} dydx

    thanks
    The inside integral is constant with respect to y, so
     \int_0^2 \left ( \int_{x^{2}-2}^x x^2 dy \right ) dx

    = \int_0^2 \left (   \left . x^2y \right |_{x^2 - 2}^x \right ) dx

    = \int_0^2 \left ( x^2((x^2 - 2) - x ) \right ) dx

    I'm sure you can finish from here.

    -Dan

    = \int_0^2 (x^4 - x^3 - 2x^2) dx
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by skystar View Post
    would i just integrate as normal, the double integral is putting me off.
    could someone show me how id do:

     \int\limits_0^2 \int\limits_{x^{2}-2}^x x^{2} dydx

    thanks
    Topsquark is right just remember that the dx,dy,d\theta d whatever dictates what the variable of integration is...whatever variable is in the integral that is not of the same type as the d whatever is considered a constant
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  4. #4
    Moo
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    Quote Originally Posted by Mathstud28 View Post
    Topsquark is right just remember that the dx,dy,d\theta d whatever dictates what the variable of integration is...whatever variable is in the integral that is not of the same type as the d whatever is considered a constant
    What are you talking about ?
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