Page 1 of 2 12 LastLast
Results 1 to 15 of 19
Like Tree6Thanks

Math Help - Green's theorem and line integral problem

  1. #1
    Newbie
    Joined
    Apr 2014
    From
    ASD
    Posts
    23
    Thanks
    1

    Green's theorem and line integral problem

    Use Green's theorem to evaluate

    $\int_{C} 3xydx+2x^{2}dy$

    Where C is the positively oriented boundary bounded by the parabola y=x^2 and y=-x

    I think I've got it set up right, but the end result is 0. Is that correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,804
    Thanks
    1576

    Re: Green's theorem and line integral problem

    You think you've set it up right? Good, what did you do to set it up?
    Thanks from vashts85
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2014
    From
    ASD
    Posts
    23
    Thanks
    1

    Re: Green's theorem and line integral problem

    Quote Originally Posted by Prove It View Post
    You think you've set it up right? Good, what did you do to set it up?
    I took the partial derivatives of 3xy (with respect to y) and 2x^2 (with respect to x), so the integral to solve is:

    $\int_0^4 \int_{x^{2}+2x}^{-x} x {d}y {d}x$

    And I ultimately get zero.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,804
    Thanks
    1576

    Re: Green's theorem and line integral problem

    I agree with your integrand but not your boundaries. Have you tried sketching the region?
    Thanks from vashts85
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2014
    From
    ASD
    Posts
    23
    Thanks
    1

    Re: Green's theorem and line integral problem

    Quote Originally Posted by Prove It View Post
    I agree with your integrand but not your boundaries. Have you tried sketching the region?
    That's because I wrote the boundaries wrong.

    The boundaries are:

    y= -x
    $y=x^{2}+2x$
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,804
    Thanks
    1576

    Re: Green's theorem and line integral problem

    Your boundaries are still wrong. Where do these graphs intersect?
    Thanks from vashts85
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Apr 2014
    From
    ASD
    Posts
    23
    Thanks
    1

    Re: Green's theorem and line integral problem

    Man it way too late for my dumb stuff.

    Here is the fixed integral:


    $\int_{-4}^0 \int_{x^{2}+2x}^{-x} x {d}y {d}x$

    Now THAT should be the correct region and should add up to zero.......maybe?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,804
    Thanks
    1576

    Re: Green's theorem and line integral problem

    Surely you can see that the graphs of $\displaystyle \begin{align*} y = x^2 + 2x \end{align*}$ and $\displaystyle \begin{align*} y = -x \end{align*}$ do NOT intersect at x = -4...
    Thanks from vashts85
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Apr 2014
    From
    ASD
    Posts
    23
    Thanks
    1

    Re: Green's theorem and line integral problem

    Quote Originally Posted by Prove It View Post
    Surely you can see that the graphs of $\displaystyle \begin{align*} y = x^2 + 2x \end{align*}$ and $\displaystyle \begin{align*} y = -x \end{align*}$ do NOT intersect at x = -4...
    Thank you, you're right. They intersect at x=-3.

    So if I just change the interval everything else is correct, yes?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Apr 2014
    From
    ASD
    Posts
    23
    Thanks
    1

    Re: Green's theorem and line integral problem

    Well, except the result, I need to reevaluate that now
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,804
    Thanks
    1576

    Re: Green's theorem and line integral problem

    Yes if you change the -4 to -3 your boundaries are now correct, so now you can correctly evaluate the line integral...
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Apr 2014
    From
    ASD
    Posts
    23
    Thanks
    1

    Re: Green's theorem and line integral problem

    Quote Originally Posted by Prove It View Post
    Yes if you change the -4 to -3 your boundaries are now correct, so now you can correctly evaluate the line integral...
    Thank you ProveIt, I am going to go to bed now but will clean it up tomorrow and post the answer.

    I appreciate your help and teaching style......much better than just someone telling it's right/wrong/giving me the answer!
    Thanks from Prove It
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,804
    Thanks
    1576

    Re: Green's theorem and line integral problem

    You're welcome I tend to be the most help to people who help themselves, so when someone has posted everything they've done it's very easy to point out what needs to be worked on
    Thanks from vashts85
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,242
    Thanks
    1795

    Re: Green's theorem and line integral problem

    You said in your original post that "C is the positively oriented boundary bounded by the parabola y=x^2 and y=-x".

    So where did x^2+ 2x come from?
    Follow Math Help Forum on Facebook and Google+

  15. #15
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,804
    Thanks
    1576

    Re: Green's theorem and line integral problem

    The OP explained in Post 5 that the original post had a typo and posted the correct bounding functions.
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. [SOLVED] Apply Green's Theorem to evaluate the integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 9th 2010, 12:55 AM
  2. Green's Theorem to evaluate an integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 30th 2009, 10:40 PM
  3. Line Integral and/or Greens Theorem Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 7th 2009, 05:12 AM
  4. Line Integral and Green's Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 4th 2009, 08:25 PM
  5. Green's Theorem Integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 4th 2009, 09:59 AM

Search Tags


/mathhelpforum @mathhelpforum