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Math Help - line integral helps

  1. #1
    n22
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    line integral helps

    Hello,
    I would very much appreciate help with this .I just dont get it .(and Im not supposed to use greens theorem)thanks.just the normal line integral.
    (2x − y + 4)dx + (5y + 3x − 6)dy around a triangle in the xy-plane
    with vertices at (0, 0), (3, 0), (3, 2), traversed in the anti-clockwise direction..
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  2. #2
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    Re: line integral helps

    Can you parameterise each of the segments that make up the triangle?
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  3. #3
    n22
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    Re: line integral helps

    Quote Originally Posted by Prove It View Post
    Can you parameterise each of the segments that make up the triangle?
    Hello!

    AB has coordinates (0,0) and (3,0)-->parametrization is x=3t

    BC has coordinates (3,0) and (3,2)-->parametrization x=3+3t,y=2t
    CO has coordinates (3,2) and (0,0)-->parametrization ,x=3;y=2
    How are my answers?
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    Re: line integral helps

    Quote Originally Posted by n22 View Post
    Hello!

    AB has coordinates (0,0) and (3,0)-->parametrization is x=3t What about the y parameterisation?

    BC has coordinates (3,0) and (3,2)-->parametrization x=3+3t,y=2t x is constant, why have you parameterised it to change?
    CO has coordinates (3,2) and (0,0)-->parametrization ,x=3;y=2 Why do you have x and y as constants when they clearly change?
    How are my answers?
    The only one I agree with is your x parameterisation for AB and your y parameterisation for BC. I also assume that the third segment should be CA, not CO.

    Also, use a different parameter for each segment.
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  5. #5
    n22
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    Re: line integral helps

    Quote Originally Posted by Prove It View Post
    The only one I agree with is your x parameterisation for AB and your y parameterisation for BC. I also assume that the third segment should be CA, not CO.

    Also, use a different parameter for each segment.

    How about this ?
    Going anticlockwise:
    for path 1:x=3t,y=o,z=0(do i need to mention this ?)
    for path2: x=3,y=2t
    for path 3:3-3t;y=2-2t
    how about t limits?
    thanks
    for
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  6. #6
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    Re: line integral helps

    Like I said, only have t as your parameter in ONE of these paths. Choose a different letter for each of the others.

    Since you know the endpoints on each interval, surely you can figure out the intervals for your parameters...
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