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Math Help - Line Integral and Green's Theorem

  1. #1
    Junior Member
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    Line Integral and Green's Theorem

    Hi,




    In this and the following problem you will consider the integral



    on the closed curve C consisting of the line segments from (0,0) to (3,4) to (0,4) to (0,0). Here, you evaluate the line integral along each of these segments separately

    Evaluate the integral above by finding the integral from (0,0) to (3,4), adding the integral from (3,4) to (0,4), and adding the integral from (0,4) to (0,0):
    = [______] + [________] + [______] = 63.9622574120271


    The answer for this problem is 63.9622574120271 and I know it because I used the green's theorem to do it. In this case they want me to do it directly and I should end up with the same value if I add the answers up.

    Please help me out....
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  2. #2
    Super Member redsoxfan325's Avatar
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    You want to parameterize each of the segments. For instance, the first segment is the line y=\frac{4}{3}x. Thus, x=t, y=\frac{4}{3}t, dx=dt, dy=\frac{4}{3}dt

    Substitute and integrate for t=0..3.

    Then do the other two segments and add up the answers.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    Solution

    See Attachment
    Attached Files Attached Files
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