In this tutorial we are going to discuss three methods of integration approximation, the Trapezoidal Rule, the Midpoint Rule, and the Left/Right Endpoint Rule. What we are going to try to do is find approximation techniques that do not rely on us being able to take the integral. The idea for all of these techniques is the same: we have a function that we want to integrate from a to b, and we start out by dividing the region between a to b into n equal partitions. So, first, we are going to talk about Trapezoidal rule. We will see graphical explanation of it, how it works and its formula. The same pattern will be used for other rules.
formulas may seem long and complicated. Instead of memorizing them,
remember the geometry on which theyre based. If you can draw the
pictures of the trapezoids and rectangles, you can probably
reconstruct the formulas quickly.
Midpoint Rule is more accurate than the Trapezoid Rule, even though
it is simpler and requires fewer function evaluations.
graphing the curve that youre estimating the area under, you can
often tell whether the estimates from the various formulas will be
higher or lower than the true area.
you will not have a graph of the function or an explicit formula.
Instead, you will use one of these Rules to estimate integrals based
on data from charts.
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.