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Integration of many variables

  1. May 11, 2009 #1
    1. The problem statement, all variables and given/known data
    F(x) = integral from x to 1 ( [tex]3t^3 - x^2 t ) dt[/tex]

    1. Calculate F'(x)

    3. The attempt at a solution

    I know the answer is

    x^3 + x.

    However, I am not sure how it is obtained.

    I know about implicit differentian, but I have never done implicit integration.

    How can you solve the problem?
  2. jcsd
  3. May 11, 2009 #2


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    Science Advisor
    Homework Helper

    In this case, you can simply work out the integral.
    Do the t-integration, it will give you
    [tex]\frac34 t^4 - \frac12 x^2 t^2[/tex]
    evaluated between the boundaries t = x and t = 1.
    Then differentiate.
  4. May 11, 2009 #3
    Thank you for your answer!

    The solution was much easier than I first thought.
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