In this lecture Professor Murray teaches you how to use the Trapezoidal Rule, Midpoint Rule, Left Endpoint Rule, and Right Endpoint Rule. With the Trapezoidal Rule, you will see its graphical representation and why a trapezoid is used. With the Midpoint Rule, you will learn why sometimes it is necessary to use midpoints as opposed to other methods. Lastly, you will finish off with the Left Endpoint and Right Endpoint 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.