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Math Help - Weird integral on assignment

  1. #1
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    Weird integral on assignment

    this integral appeared on an online assignment, but im really having troubles figuring out the domain region D on this. I could simply use the upper and lower limits to sketch the domain D. However, the '7y' component is ticking me off, why cant dy vary from 7x to 7 for example??? i need to know this because i need to reverse the order of integration to dydx and to do so, i need to learn how to set up the limits for the new iteration.
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  2. #2
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    Isn't it as simple as

    I=\int_0^1\int_{7y}^7 e^{x^2}dxdy
    I=\int_0^1 \left[2xe^{x^2}\right]_{7y}^7dy
    I=\int_0^1 14e^{49}-14ye^{49y^2}dy

    ?
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  3. #3
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    Hello, ramzouzy!

    \int^1_0 \int^7_{7y} e^{x^2}\,dx\,dy

    The limits are: . \begin{array}{ccc}y\:=\:1 & & x \:=\:7 \\ y\:=\:0 & & x \:=\:7y \end{array}

    The region looks like this:
    Code:
            |
           1|               * (7,1)
            |           *:::|
            |       *:::::::|
            |   *:::::::::::|
        - - * - - - - - - - + - -
            |               7

    Reversing the order, we have: . \int^7_0 \int^{\frac{x}{7}}_0 e^{x^2}\,dy\,dx

    Can you finish it?

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