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Homework Help: 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


    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


    User Avatar
    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.
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