# Math Help - Integral and trapezoidal sum

1. ## Integral and trapezoidal sum

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

$
J = \int_0^{{\pi}\over{4}} {{1} \over {5 - 2\sin{x}}} dx
$

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?

$
\ln \left | {5 - 2\sin{x}} \right |
$

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

$
{{{\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}}
$

2. 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.