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Math Help - setting up integral (volume)

  1. #1
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    setting up integral (volume)

    Find the volume of the following solid, bounded by the surfaces:

    z = x + e^y,
    z = 0,
    y = x^2 + 1
    and x + y = 3

    Note* just set up the integral, do not evaluate
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  2. #2
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    Quote Originally Posted by boousaf View Post
    Find the volume of the following solid, bounded by the surfaces:

    z = x + e^y,
    z = 0,
    y = x^2 + 1
    and x + y = 3

    Note* just set up the integral, do not evaluate
    Have you drawn a rough sketch?

    More than one correct answer is possible. Here's one such:

    V = \int_{x=a}^{x=b} \int_{y=x^2 + 1}^{y=-x+3} \int_{z=0}^{z = x + e^y} dz \, dy\, dx

    where a and b are the x-coordinates of the intersection points of y=x^2 + 1 and y = -x + 3.
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  3. #3
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    thanks mr fantastic! very helpful
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