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Math Help - Integration by parts (long question)

  1. #1
    Junior Member
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    Integration by parts (long question)

    I've been able to solve parts A, B, and D of this question. But I'm really stuck on Part C. Could someone offer some insight?



    Part A:

    This follows from integration by parts:

    u = f(x), v=x
    du = f'(x), dv = dx

    Part B:

    Substitute y=f(x), dy = f'(x). It follows that x=g(y). Then we substitute values into formula from part A, remembering to change the bounds: When x=a, y = f(a). When x=b, y = f(b).

    Part c:

    Stuck on this.

    Part d:

    Using formula from Part B, we simply plug in values and find that the integral evaluates to 1.

    Thanks,
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  2. #2
    MHF Contributor
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    Re: Integration by parts (long question)

    Here it is with the variables chosen/labelled slightly different. I also have this



    Will link to the thread if I find it.
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