4.6 Numerical Integration

The Trapezoidal Rule

One method to approximate a definite integral is to use n trapezoids.

The Trapezoidal Rule

Example:

Simpson’s Rule One way to view the trapezoidal rule if to say that on each subinterval, you approximate f by a 1 st degree polynomial. In Simpson’s Rule, you approximate f by a 2 nd degree polynomial.

Simpson’s Rule For Simpson’s Rule, we are still going to partition [a,b] into n subintervals, but n must be even! We will look at 2 subintervals at a time and create a 2 nd degree polynomial, p, that passes through (x o, y o ), (x 1, y 1 ), and (x 2, y 2 ). Then,

Example: