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Math Help - Problem with a Double Integral

  1. #1
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    Problem with a Double Integral

    Hi everybody,

    Basically a simple double integral problem (see attached). However, is it correct that for Double Integrals, there are always (?!) two possible ways to get the solution. For the attached problem, I don't get the same result on the alternative way (and the result is obviously wrong). What am I doing wrong? How to choose the boundaries..?

    Thanks for your help!
    Attached Thumbnails Attached Thumbnails Problem with a Double Integral-problem-double-integral.jpg  
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  2. #2
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    Re: Problem with a Double Integral

    No, there's not always two ways to evaluate a double integral.

    Consider for example \displaystyle \begin{align*} \int_0^3{\int_{x^2}^0{x^3e^{y^3}\,dy}\,dx} \end{align*}.

    The integration can not be performed as is, but the integral CAN be evaluated if the order of integration is reversed.

    So there is only ONE way to evaluate this integral.
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  3. #3
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    Re: Problem with a Double Integral

    Thanks!

    So for my above example, there is only one way to solve it?

    Is there a method, any hint, to see in which order the integrals should be defined?

    Thanks!
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  4. #4
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    Re: Problem with a Double Integral

    Quote Originally Posted by Marmy View Post
    Thanks!

    So for my above example, there is only one way to solve it?

    Is there a method, any hint, to see in which order the integrals should be defined?

    Thanks!
    You have drawn your region incorrectly. Fix that before you try to change the order of integration. You will also find that when you reverse the order, in this case you will need to split your integral into two pieces.
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