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    This is from the Heinneman textbook. If I'm lucky, maybe it'll be another misprint:

    "Use the substitution x=1/u to find the value of ∫(ln x*[1+x²]-1)dx between 2 and 1/2"

    Now, when you use the substitution, you end up with -∫(ln u*[1+u²]-1)dx between 1/2 and 2. This is exactly the same as the first integral, except with a minus sign in front of it and the limits swapped round, so the subsitution seems pretty pointless.

    The correct answer is 0. Can somebody explain how to get to it? Thanks.
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    sorry, i tried it, but i'm not clever enough.
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    Use the fact that:
    ab f(x) dx = - ba f(x) dx

    Your substitution showed that:
    I = -I

    So I must be zero.
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    (Original post by dvs)
    Use the fact that:
    ab f(x) dx = - ba f(x) dx

    Your substitution showed that:
    I = -I

    So I must be zero.
    Great - thanks, I thought it was something like that, but I couldn't work out how to show it in a decent way.
 
 
 
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