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Line integral question, answer is here, just confused on it

  1. Mar 24, 2007 #1
    Hello everyone i'm confused on this line integral.
    The substiution is easy but i'm not sure where 2t is coming from...

    integral over C x^2*y*sqrt(z) dz;
    C: x = t^3;
    y = t;
    z = t^2;

    0 <= t <= 1

    integral over C x^2*y*sqrt(z) dz =
    integral 0 to 1 (t^3)^2 (t) sqrt(t) * 2t dt =
    integral 0 to 1 2*t^9 dt;

    Okay I see they are just plugging in the t's for the x,y,z, but why do they write sqrt(t)? the sqrt(t^2) is just t.

    Also where is this 2t dt coming from?

    I thought maybe they used: sqrt(t^2); u = t^2;
    du = 2t dt;
    1/2*du = t dt;


    Thanks
     
  2. jcsd
  3. Mar 24, 2007 #2
    I guess sqrt(t) is just a typo. It should be sqrt(t^2) (Note that the final integral is t^9). And that 2tdt is equal to the differential dz.
     
  4. Mar 24, 2007 #3
    What Neutrino said. The final integrand should be 2t^9. In fact, if you compare step 2 to step 3, you'll find that it does not logically follow. So in all likelihood it was a typo.
     
  5. Mar 27, 2007 #4
    THanks for the help guys!
     
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