Educator

Trapezoidal Rule, Midpoint Rule, Left/Right Endpoint Rule

Main formula:

Trapezoidal Rule:

Midpoint Rule:

where,

Left/Right Endpoint Rules:

where for the Left Endpoint Rule,

For the Right Endpoint Rule,

Hints and tips:

• These formulas may seem long and complicated. Instead of memorizing them, remember the geometry on which they’re based. If you can draw the pictures of the trapezoids and rectangles, you can probably reconstruct the formulas quickly.

• The Midpoint Rule is more accurate than the Trapezoid Rule, even though it is simpler and requires fewer function evaluations.

• By graphing the curve that you’re estimating the area under, you can often tell whether the estimates from the various formulas will be higher or lower than the true area.

• Sometimes 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.