1. 1 Numerical Integration Section 4.6

2. 2 Why Numerical Integration? Let’s say we want to evaluate the following definite integral:

3. 3 Numerical Integration There are many functions whose antiderivatives cannot be found. To find the definite integral of these functions, we will use one of the approximation techniques. Using Trapezoids Area of a trapezoid A =

4. 4 Trapezoid Rule In general, for n trapezoids, Pattern: The coefficients in the Trapezoid Rule are 1 2 2 2 … 2 2 1

5. 5 Example Use the Trapezoid Rule to approximate the definite integral. (w/ n = 4)

6. 6 Simpson’s Rule n is even Pattern: The coefficients in Simpson’s Rule are 1 4 2 4 2 … 4 2 4 1

7. 7 Example Use Simpson’s Rule to approximate the definite integral. (w/ n = 4) Check it out on the calculator.