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Math Help - Line integral

  1. #1
    Super Member angel.white's Avatar
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    Line integral

    Evaluate the line integral, where C is the given curve.

    \int_C xy~dx + (x-y)~dy C consists of line segments from (0,0) to (2,0) and from (2,0) to (3,2)

    can someone help me set this up properly? I thought I was doing it right, but seem to be getting incorrect answers.

    Also, latex doesn't seem to like this format or something, but the actual integral is: the integral over the curve of xy dx + (x-y) dy
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by angel.white View Post
    Evaluate the line integral, where C is the given curve.

    \int_C xy~dx + (x-y)~dy C consists of line segments from (0,0) to (2,0) and from (2,0) to (3,2)

    can someone help me set this up properly? I thought I was doing it right, but seem to be getting incorrect answers.

    Also, latex doesn't seem to like this format or something, but the actual integral is: the integral over the curve of xy dx + (x-y) dy
    Since latex isn't working, I wrote it out...



    Hopefully this is still legible... :-|

    Can you take it from here?

    --Chris
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  3. #3
    Super Member angel.white's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Since latex isn't working, I wrote it out...



    Hopefully this is still legible... :-|

    Can you take it from here?

    --Chris
    Thank you very much, Chris. However, as I understand it, this problem only has lines from (0,0) to (2,0) and from (2,0) to (3,2) but not from (0,0) to (3,2)
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by angel.white View Post
    Thank you very much, Chris. However, as I understand it, this problem only has lines from (0,0) to (2,0) and from (2,0) to (3,2) but not from (0,0) to (3,2)
    Alright, I think we can fix that...



    I think I got this...

    I hope you can follow this!

    --Chris
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  5. #5
    Super Member angel.white's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Alright, I think we can fix that...



    I think I got this...

    I hope you can follow this!

    --Chris
    Thank you ^_^

    I'm not sure where my discrepancy has been, perhaps in converting to vectors, I had just kept everything in terms of x, that could be it. Or maybe my mind is disorganized and I errored somewhere along the line.

    Also, for C2, I got \int_0^1 xy dx = 8/3
    then 0+0+8/3 + 3 = 17/3

    Which my book likes.

    I appreciate it, there is always 1 or 2 problems which just drive me nuts. I think if I solve it wrong the first time, I'm more and more likely to solve it wrong the subsequent times.
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by angel.white View Post
    Thank you ^_^

    I'm not sure where my discrepancy has been, perhaps in converting to vectors, I had just kept everything in terms of x, that could be it. Or maybe my mind is disorganized and I errored somewhere along the line.

    Also, for C2, I got \int_0^1 xy dx = 8/3
    then 0+0+8/3 + 3 = 17/3

    Which my book likes.

    I appreciate it, there is always 1 or 2 problems which just drive me nuts. I think if I solve it wrong the first time, I'm more and more likely to solve it wrong the subsequent times.
    Woops! I forgot that 8/3 part [you tend to overlook things when you're dead tired. >_> ] ...at least you got the answer now!

    --Chris
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