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Math Help - Calculating the value of an integral given some properties

  1. #1
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    Calculating the value of an integral given some properties

    Hi, I have done all the exercises I have to do for tomorrow, but I am stuck on this one...my professor said it is really easy, but I have no clue how to solve this . Any help would be very much appreciated, thanks!

    Given the following:
    u(a)=-4, u'(b)=-4, u'(a)=-1, u(b)=-4
    v'(a)=-8, v(b)=3, v(a)=4, v'(b)=2

    \int^b_a u(x) v(x) dx = 4, \int^b_a u(x) dx = 3
    \int^b_a v'(x) dx = -1, \int^b_a u'(x) v(x) dx = -6

    What is the value of \int^b_a u(x) v'(x) dx?
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  2. #2
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    By by-parts:

    \displaystyle \int_{a}^{b}u(x)v'(x)\;{dx} = u(x)v(x)\bigg|_{a}^{b}-\int_{a}^{b}u'(x)v(x)\;{dx}
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  3. #3
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    Thanks a lot!
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