Answer Happy

You may use matlab
Consider the integral [ Væe" dt = 1.25563 00825 51864. (a) Evaluate using the midpoint rule with a sequence of doubling n's, and find the errors. Take the ratios of errors. Are they four as expected? (b) Can you explain why the errors are not behaving as expected? Hint: remember that f"(e) = f" (d;) where each d, e [26-1, 06]. n = n i=1 (c) Apply the substitution x = uz (or u = vx) to the integral. Then try the midpoint rule again, listing errors. Why do you think it is working well this time?