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How to evaluate this definite integral?

  1. Nov 22, 2015 #1
    Hello, I don't know how to approach this problem, provided in the image below:


    I am assuming that in order to solve this problem, you have to transform the 2nd integral into the form of the first integral, but I am not sure if that's even the way to solve it, and even if it was, I don't know how to transform it. Any help would be appreciated.

    Thanks :-)
  2. jcsd
  3. Nov 22, 2015 #2


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    Staff Emeritus
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    Have you studied u-substitution for indefinite integration yet?
  4. Nov 22, 2015 #3
    We learned about it a few days ago... I don't know what to substitute to solve the problem :-(
  5. Nov 22, 2015 #4
    Ohh ok I see I see

    so you let u = sqrt(x), then x = u^2, so that du = 2u du

    Then you plug them into the 2nd integral, and then you get integral of f(u) / u * 2u du, which then simplifies into 2 * integral of f(u) du, which is 3, as given by the first integral, so that the answer is 2*3 = 6.

    Is this right? O_O
  6. Nov 22, 2015 #5


    Staff: Mentor

    So dx = 2udu...

    In the future, please post questions like this one in the Homework & Coursework section, not here in the math technical sections.
  7. Nov 22, 2015 #6
    Thanks for your help :-) And yes I will make sure to post similar questions to the appropriate sections. Apologies for the inconvenience
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