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Math Help - Solving Integral

  1. #1
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    Feb 2010
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    Solving Integral

    I don't understand integration and differentiation very well, could someone please explain how this is true;



    Thanks.
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  2. #2
    MHF Contributor
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    Note that \frac{d}{dx} \ln x = \frac{1}{x}.

    The Fundamental Theorem of Calculus states that if F'(x) is the derivative of F(x), then \int _a ^b F'(x) \cdot dx = F(b) - F(a).

    In your question, this means \int _{0.025} ^{0.075} \frac{1}{r} \cdot dr = \ln (0.075) - \ln (0.025), which is \ln \left(\frac{0.075}{0.025}\right) by the rules of logarithms.
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  3. #3
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    That's great, thanks for your help!

    I need to learn the rules of calculus!
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