4. Use Simpson’s Rule with n = 10 to approximate the value of

Question

4. Use Simpson’s Rule with n = 10 to approximate the value of ln(5/4) using the integral

Answer 1

Divide the interval [4,5] into 10 equal subintervals, each of length (5-4) / 10 = 0.1. Let f(x) = 1/x

Then, using Simpson's Rule, the value of the integral is approximated by:

[(5-4) / (3(10))][f(4) + 4f(4.1) + 2f(4.2) + 4f(4.3) + 2f(4.4) + ... + 4f(4.9) + f(5)]

= (1/30)[1/4 + 4(1/4.1) + 2(1/4.2) + ... + 4(1/4.9) + 1/5] = 0.22314