1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Can someone just check if I did this line integral correctly?

  1. Nov 7, 2013 #1
    1. The problem statement, all variables and given/known data

    S4Fimyg.png

    2. Relevant equations



    3. The attempt at a solution

    $$\int _{ 0 }^{ 2\pi }{ xdx } \\ =-\int _{ 0 }^{ 2\pi }{ sintcostdt } \\ =0$$

    It feels wrong.
     
  2. jcsd
  3. Nov 7, 2013 #2
    I got zero also using a different method. Let's review the steps. You said
    x = cos t, dx = -sint dt and t now runs from 0 to 2##\pi##.

    Since cost and sint are both periodic in 2##\pi## you got zero.

    What may feel wrong is that ##\int_0^{2\pi}x dx## is not zero. However, this is not the same thing as integrating x around a circle. Basically you are running cos(t) around that circle, and it's going to start and end with the same value.
     
  4. Nov 8, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Notice that x is positive on the right side of the circle, negative on the left side of the circle. The two halves cancel, leaving 0.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Can someone just check if I did this line integral correctly?
Loading...