In this lesson we are going to talk about Simpson's Rule. Simpson's Rule is a way of estimating the value of an integral when you cannot solve it by traditional integration techniques. We already learned a few of those; the Trapezoidal Rule, the Midpoint rule, and the Left and Right Endpoint Rules. Simpson's Rule is based on the same kinds of ideas but it is a little more sophisticated. We will see later on that the answers it gives are a lot more accurate. We are going to do several examples to see how this rule works.
the formulas for the Trapezoid, Midpoint, and Left and Right
Endpoint Rules, this formula is too complicated to derive on the
spot, so it is probably worth memorizing.
to remember the pattern of the coefficients, it helps to remember
that it comes from adding up overlapping sets of the form 1-4-1:
1 - 4 - 1
1 - 4 - 1
1 - 4 - 1, etc.
Rule is much more accurate than any of the Trapezoid,
Midpoint, and Left and Right Endpoint Rules, especially for bigger
values of n. However, it still takes about the same number of
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.