1. Numerical Integration
4.6
Numerical Integration
Trapezoidal Rule
Area of a Trapezoid b2 h b1
b b2 h

2. We are going to sum up
n trapezoids from a to b.
Let’s let n = 4
(4 trapezoids)
Now we need to find the
sums of the area of these
four trapezoids. a h b
x x1 x x x4
simplified to

3. The bigger n you use, the more accurate your answer
will be.

4. Use the Trapezoidal Rule to approximate1

5. 1 4 2 4 2 4 … 4 2 4 2 4 1 Simpson’s Rule n is even
Note: The coefficients in Simpson’s Rule have the following
pattern …

6. Ex.
Let n = 4
if n = 8