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Math Help - U Substitution

  1. #1
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    U Substitution

    I'm having difficulties figuring out what this is asking. This is what I gather so far.

    u = x^2
    du = 2x dx
    dx = 1/2u du

    Then I don't know how to apply it.U Substitution-untitled.png
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  2. #2
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    Re: U Substitution

    I figured it out by multiplying 1/3 to 6 from f(x)dx = 6. I don't know why I needed to do that though.
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  3. #3
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    Re: U Substitution

    u = x^2
    du = 2x dx
    (1/2)du = x dx

    Now, substitute u for x^2 and (1/2)du for x dx. Change your bounds in terms of u (which conveniently become the bounds in the first integral). Your integral is now identical to the first integral with the exception of it being in terms of u and the 1/2 constant out front. Your answer then becomes (1/2) * 6 = 3.
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