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Math Help - Finding area of region bounded by graphs.

  1. #1
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    Finding area of region bounded by graphs.

    Hi, I have been having trouble finding areas of region bounded by graphs.
    Like for example:
    y=xe-(x^2/2), y=0, x=0, x=√2
    and
    y=3x, y=0, x=0, and x=3

    So for example, the second one.
    First I would graph it.
    Then I would find out the axis it gets cut off right? From which x it starts, and the x it ends.
    So then it would be [0, 3]
    Then I would use the y=3x right? As the integral.
    Then it would be (1/(3-0))∫3x
    =1/3∫3x
    Then I would find the antiderivative?
    Which would equal 1/ln3 * 3x = 3x/ln3
    Then I would plug in the points 3 and 0 right and subtract it from each other?

    So 1/3[(3(3)/ln3)-3(0)/ln3]
    Which is kind of not a pretty number... but is this the right process?

    Just making sure before I do the first one... because the antiderivative of xe-(x^2/2) looks a bit difficult.

    So can anyone make sure if these steps are right? Thanks!
    And if it really is wrong, explain the process or some advices as well? Thanks!
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  2. #2
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    Re: Finding area of region bounded by graphs.

    The integral of xe^-(x^2/2) is quite simple. just put -x^2/2 = t , we get -xdx = dt
    The given integral becomes - e^t dt which is -e^t
    Now you can proceed further.
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