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    Not sure how to go about answering this question and whether it requires parameterization. I need to evaluate the line integral of  (y-y^2)i + (x-2xy)j +k where c is two line segments from (0,1) to (2,1) and from (2,1) to (2,3), picture above
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    (Original post by BinaryJava)
    Attachment 697258
    Not sure how to go about answering this question and whether it requires parameterization. I need to evaluate the line integral of  (y-y^2)i + (x-2xy)j +k where c is two line segments from (0,1) to (2,1) and from (2,1) to (2,3), picture above
    This doesn't seem to need any parameterisation. You have a line of constant y followed by a line of constant x, so along the first line, you can substitute in the value of y and integrate against x, and vice versa for the second.
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    (Original post by atsruser)
    This doesn't seem to need any parameterisation. You have a line of constant y followed by a line of constant x, so along the first line, you can substitute in the value of y and integrate against x, and vice versa for the second.
    But you need to know what the "d..." bit is, surely? If it's an integral w.r.t. ds, for example, this would be quite different from a ".dr" integral, for example.
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    (Original post by DFranklin)
    But you need to know what the "d..." bit is, surely? If it's an integral w.r.t. ds, for example, this would be quite different from a ".dr" integral, for example.
    From the limited part of the question that I could see, I guessed that it's a .d\bold{r}
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    (Original post by atsruser)
    From the limited part of the question that I could see, I guessed that it's a .d\bold{r}
    Yes its a dr, do you split it into two parts?
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    (Original post by BinaryJava)
    Yes its a dr, do you split it into two parts?
    Yes, you split it into 2 parts.

    e.g. for the first part, we have r going from (0, 1) to (2, 1). For notation later, call this part of the curve C_1

    You ask if this requires parameterization; you can "kind of " avoid parameterization by using the x-coordinate itself as a parameterization, but until you are confident with what is going on, I would use a formal parameterization.

    So parameterize with t; we want r = (0, 1) when t =0 and (2, 1) when t = 1, so we can write r = (2t, 1).

    Then you can rewrite \displaystyle \int_{C_1} {\bf F . dr} as \displaystyle\int_{t=0}^{t=1} {\bf F .} \dfrac{d{\bf r}}{dt}\, dt, which will leave you with a standard (A-level style) integral.

    Do the same thing for the 2nd part of the curve and then add them together.
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    (Original post by DFranklin)
    Yes, you split it into 2 parts.

    e.g. for the first part, we have r going from (0, 1) to (2, 1). For notation later, call this part of the curve C_1

    You ask if this requires parameterization; you can "kind of " avoid parameterization by using the x-coordinate itself as a parameterization, but until you are confident with what is going on, I would use a formal parameterization.

    So parameterize with t; we want r = (0, 1) when t =0 and (2, 1) when t = 1, so we can write r = (2t, 1).

    Then you can rewrite \displaystyle \int_{C_1} {\bf F . dr} as \displaystyle\int_{t=0}^{t=1} {\bf F .} \dfrac{d{\bf r}}{dt}\, dt, which will leave you with a standard (A-level style) integral.

    Do the same thing for the 2nd part of the curve and then add them together.
    I will give that a crack tomorrow, out of interest how would the non parametrization work?
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    (Original post by BinaryJava)
    I will give that a crack tomorrow, out of interest how would the non parametrization work?
    You are integrating along lines of constant x and constant y, so you can set x and y to the appropriate constant and integrate against the other variable. For practice though I would agree that it's best just to parameterise.
 
 
 
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