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Math Help - integral problem

  1. #1
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    integral problem

    If h(x)=dg(x)/dx is integrable on the closed interval [a,b], then the integral from a to b of g(x)h(x)dx = ? and it must be in terms of f, g, a, and b
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by chaddy View Post
    If h(x)=dg(x)/dx is integrable on the closed interval [a,b], then the integral from a to b of g(x)h(x)dx = ? and it must be in terms of f, g, a, and b
    note that if h(x) = \frac d{dx}g(x), then \int h(x)~dx = g(x) + C

    Thus, using integration by parts, taking u = g(x) and dv = h(x), we have:

    \int_a^b g(x)h(x)~dx = \left. g(x)g(x) \right|_a^b - \int_a^b g'(x)g(x)~dx

    i leave the rest to you
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