Study Guide

Definite Integrals Topics

Left-Hand Sum

We have formulas to find areas of shapes like rectangles, triangles, and circles (pi, anyone?)....

Right-Hand Sum

There is much debate about who is more awesome...right-handers or south-paws. Would you want...

Comparing Right- and Left-Hand Sums

Left Hand Sums and Right Hand Sums give us different approximations of the area under of a curve....

Midpoint Sum

We're driving along from right coast to the left coast, and now it's time to take a rest stop at...

Trapezoid Sum

All of these summations are starting to feel like Rube Goldberg Machines. Granted, Rube Goldberg...

Comparison of Sums

You'll probably get asked to compare the accuracy of different types of sums. Here are the main...

Definite Integrals of Non-Negative Functions

When f is a non-negative function and a < b, the area between the graph of f and the...

Definite Integrals of Real-Valued Functions

When we're integrating a non-negative function from a to b, the integral

Properties of Definite Integrals

There are a lot of useful rules for how to combine integrals, combine integrands, and play with...

Average Value

We know how to take the average of a group of numbers: add all the numbers and divide by how...

In the Real World

Remember all that stuff about left-hand sums and right-hand sums? That's why your calculator...