Simpson's rule

Question

Use Simpson's rule to estimate using 4 intervals:

∫(from 1 to 3) e^x^2 dx

Answer 1

Let f(x) = e^{x^2}

 

Divide the interval [1,3] into 4 equal parts.  The length of each part is Δx = (3-1)/4 = 1/2.  The resulting subintervals are:

 

l_____l_____l______l_____l

1       1.5      2         2.5      3

 

By Simpson's Rule, 

 

∫e^{x^2}dx ≈ (3-1)/(3•4)[f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + f(3)]

 

              = (1/6)[10325.00075] = 1720.8