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Math Help - Integral and trapezoidal sum

  1. #1
    Junior Member
    Joined
    May 2009
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    Integral and trapezoidal sum

    I need to use the trapezoidal sum (T2) to find an approximation to:

    <br />
J = \int_0^{{\pi}\over{4}} {{1} \over {5 - 2\sin{x}}} dx<br />

    Firstly, how would I go about integrating this problem? I know ln would be involved, but I'm not really sure where to go from there. Would this be correct?

    <br />
\ln \left | {5 - 2\sin{x}} \right |<br />

    Now, with the trapezoidal sum, I haven't really been able to find good examples, but would this be correct (in theory)?

    <br />
{{{\pi}\over{4}}\over{2}}\cdot{{J(0) + J({{\pi}\over{8}})}\over{2}}+ {{{\pi}\over{4}}\over{2}}\cdot{{J({{\pi}\over{8}}) + J({{\pi}\over{4}})}\over{2}}<br />
    Last edited by drew.walker; August 10th 2009 at 04:26 AM.
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  2. #2
    Senior Member
    Joined
    Jan 2009
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    You cannot integrate like that. (Think of the \ln differentiation rule)

    I can't think of a way to integrate that yet. I just want you to know that your integration is wrong.
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