I'm trying to estimate the value of the following integral on the interval $[0,1]$
$ I = \int_0^1 \frac{1}{1+x} dx $
So, using the composite trapezoid rule (and with $n=4$, ie I'm only using the first 4 $x_i$ to do the approximation), I get the following expression:
$ I = \frac{67}{60} - \frac{1}{96} (2(1+\xi_1)^{-3} + 2(1+\xi_2)^{-3} + 2(1+\xi_3)^{-3} + 2(1+\xi_4)^{-3}) $
But I'm lost when it comes to calculating the error and finding a value for $\xi$. What's the general way of finding the error like this?
Formula I'm using
I = \frac{h}{2} \sum_{i=1}^n [f(x_{i-1}) + f(x_i)] - \frac{h^3}{12} \sum_{i=1}^n f^{''}(\xi_i)