# Question 1

Approximate the integral of f(x) = e^{-x} on [0, 10] using
Simpson's Rule and Simpson's 3/8 Rule.

Answer: 1.711661979876841 and 1.388606601719423.

# Question 2

Approximate the integral of f(x) = x^{2} on the interval [0, 2]
using Simpson's Rule and Simpson's 3/8 Rule.

Answer: 8/3 (or 2.666666666666667) in both cases.

# Question 3

Approximate the integral of f(x) = x^{4} on the interval [0, 2]
using Simpson's Rule and Simpson's 3/8 Rule.

Answer: 20/3 = 6.666666666666667 and 176/27 = 6.518518518518516.

# Question 4

What is the estimated error for the approximation in Question 3 what is the actual error? Is this exact, and why?

Answer: Because the 4th derivative is a constant, the errors may be found exactly: -4/15 and -16/135.

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.