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Line integral over a given curve C

  1. Dec 5, 2014 #1
    1. The problem statement, all variables and given/known data
    Evaluate the line integral over the curve http://webwork.math.ttu.edu/webwork2_files/tmp/equations/33/92ca0e3b907f876e5a974ad1457d1f1.png [Broken] from 7c0c57c09fd2ddefc5e4bd47ccf5351.png to http://webwork.math.ttu.edu/webwork2_files/tmp/equations/6f/bccf9dd59b9c22450c590a042bb77d1.png [Broken].

    ∫-ydx+3xdy (over the curve C)

    2. Relevant equations

    3. The attempt at a solution
    I'm really stuck on this problem not doing very well with line integrals.
    I started by changing y^2=x to parametric --> x=t^4 y=t^2
    Then I took the derivate of each one --> dx=4t^3dt dy=2tdt
    I then plugged in each term into the given integral --> ∫-ydx+3xdy (over the curve C) = ∫-(t^2)(4t^3)+3(t^4)(2t)dt

    Would I use the points given to get my limits of integration or am I way off?
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Dec 5, 2014 #2


    Staff: Mentor

    A simpler set would be x = t2, y = t. You can use the given points on C to figure out the interval for t values.
    Last edited by a moderator: May 7, 2017
  4. Dec 5, 2014 #3
    Got it,
    Thank you!
  5. Dec 5, 2014 #4


    User Avatar
    Homework Helper

    You could have just chosen ##x = y^2## and ##y = y## (where ##y## is the parameter). Then you can see that ##1 \leq y \leq 3##.

    Then computing ##\frac{dx}{dy} = 2y## will give you ##dx = 2y dy##.

    Subbing everything in you should find the same answer.
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