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Math Help - Calc: Substitution Rule

  1. #1
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    Calc: Substitution Rule

    the problem is Sin(x^3) x^2 dx

    u = x^3
    du = 3x^2

    I noticed when my teacher was solving this out her final answer was -1/3 cos(x^3) + C

    My question is where did the x^2 go and where did she pull out the 1/3 from?
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  2. #2
    Senior Member vincisonfire's Avatar
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      sin(x^3) x^2 dx *
    With the substitution you proposed you have
     u = x^3
     \frac{du}{3} = x^2 dx And the expression becomes   sin(u) \frac{du}{3}
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  3. #3
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    I'm sorry but why is it dU/3? where did you get that?
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  4. #4
    Senior Member vincisonfire's Avatar
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     d(u) = du

     d(u) = d(x^3) = 3x^2 dx = du

    If you divide the two last term by 3 you get

     x^2 dx = \frac{du}{3}
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