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I need help taking the antiderivative.

  1. Mar 14, 2009 #1
    3 sin ^2 t cos t (i) + 3 sin t cos^2 t (j) + 2 sin t cost (k)

    I have to take the antiderivate for each Vector.

    Then I have to evaluate it from pi/2 to o.

    I'm confused because I can't use a trigonometric substitution.

    Cosine is odd for the I vector but I can't substitute 1-sin^2 t in for it. Because it has to be cos^2 t
  2. jcsd
  3. Mar 14, 2009 #2


    User Avatar
    Homework Helper

    for the i component, try a substitution since d/dt(sint)=cost, similiar with the other two components.
  4. Mar 14, 2009 #3
    I get it. If I make it like this, Sin (t) * Sin (t) * Cos (t) dt

    t= sin (t)
    dt = cos t)

    it becomes t*t dt

    then it becomes t^2 dt

    and the integral of this is t^3 / 3
  5. Mar 14, 2009 #4


    Staff: Mentor

    Use a different variable or you'll really confuse yourself.
    u = sin(t), du = cos(t)dt

    So the integrand sin2(t) cos(t) dt becomes u2 du
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