- 1)
- (10 pts) It can be proved mathematically that
*absolute error*for Simpson's rule is bounded by

Write a short technical report that verifies this error bound for the integral

An outline of this process is as follows:

- a)
- Assume the desired
*absolute error*is 10^{-6}. - b)
- Determine the value of
*n*necessary to achieve this error. Note that you need the smallest value for*n*that works. - c)
- Determine the corresponding value for
*h*once the required*n*is known. - d)
- Create a table of |f''''(
*x*)| and use this to estimate the maximum value of |f''''(*x*)| over the range of integration. - e)
- Compute the right side of the error inequality.
- f)
- Verify that the quantity you computed in step e) is greater than the absolute error for your integral approximation.

2017-11-06