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Math Help - Line integral

  1. #1
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    Line integral

    Could use some help in evaluating this line integral....

    <br />
\int\limits_\Upsilon {\{ [\exp (x^2 /y^2 ) + xy^2 ]dx + [(y^6 /x) + (x/y^3 )]dy\} } <br />

    where the path r is the line {y^2 } = x, from (1,1) to (4,2)
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  2. #2
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    Quote Originally Posted by reivera View Post
    Could use some help in evaluating this line integral....

    <br />
\int\limits_\Upsilon {\{ [\exp (x^2 /y^2 ) + xy^2 ]dx + [(y^6 /x) + (x/y^3 )]dy\} } <br />

    where the path r is the line {y^2 } = x, from (1,1) to (4,2)
    First you need to parameterize the curve

    let y=t then x=t^2 t \in [1,2]

    Note: there are many other ways we have parameterized this.

    Now we can compute dy and dx

    dx=2tdt \mbox{ and } dy=dt

    now we just substitute in to the above and evalute

    \int_{1}^{2}\left( e^{t^2}+t^4\right)(2t)dt+\left( t^4+\frac{1}{t}\right)dt

    Now it is off to the races.

    Good luck.
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