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Math Help - Double Integral over a region

  1. #1
    M.R
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    Double Integral over a region

    Question: Let R be the region in the plane defined by:

    R = \{(x,y) \in R^2 : 1\leq x \leq 2, x\leq y \leq x^3 \}

    Calculate:

    \int \int_R e^{\frac{y}{x}} dA


    My attempt:

    \int_1^2 \int_x^x^3 e^{\frac{y}{x}}  dy  dx = \int_1^2 x e^x^2 - xe dx

    = \frac{1}{2}[e^x^2 - x^2e]_1^2 = \frac{1}{2}e^4 - 2e

    Can someone please verify if my answer is correct? Thank you
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  2. #2
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    Re: Double Integral over a region

    Quote Originally Posted by M.R View Post
    Question: Let R be the region in the plane defined by:

    R = \{(x,y) \in R^2 : 1\leq x \leq 2, x\leq y \leq x^3 \}

    Calculate:

    \int \int_R e^{\frac{y}{x}} dA


    My attempt:

    \int_1^2 \int_x^x^3 e^{\frac{y}{x}}  dy  dx = \int_1^2 x e^x^2 - xe dx

    = \frac{1}{2}[e^x^2 - x^2e]_1^2 = \frac{1}{2}e^4 - 2e

    Can someone please verify if my answer is correct? Thank you
    Yes it's correct
    Thanks from M.R
    Follow Math Help Forum on Facebook and Google+

  3. #3
    M.R
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    Re: Double Integral over a region

    Thank you
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