I am working on question 4 for the first set of homework and am not sure I am getting the correct graphs.

For the analytical integration error I substituted the sinh(x) in the integral with x - x^3/3! + x^5/5! and then computed the integral of sin(x) - (x - x^3/3! + x^5/5!) from 0 to xi.

For the approximate integration error my change of variable equation was x(xi) = xi^2 + xi. For the summation of sinh(xi)*W, I again substituted x - x^3/3! + x^5/5! for sinh(x) and then plugged in my x(xi) equation for x. Then I performed quadrature for n=1,2,3 and subtracted those results (0,0.5483, 0.4484 respectively) from the integral of sin(x) from 0 to xi. The graphs don’t really look like what I was expecting.