Usually the first application of integration is to find the area bounded by a function and the *x*-axis, followed by finding the area between two functions. We begin with these problems

**First some calculator hints**

Graphing Integrals using a graphing calculator to graph functions defined by integrals

Graphing Calculator Use and Definition Integrals – Exam considerations Suggestions for using a calculator efficiently in area/volume problems

**Area Problems**

Area Between Curves

Under is a Long Way Down How to avoid “negative area.”

Density Functions Not often asked on the AP exams, but a good application related to area, nevertheless.

Who’d a thunk it? Some more complicated area problems for CAS solution.

Improper Integrals and Proper Areas – a BC topic

**Average Value**

Average Value of a Function

What’s a Mean Old Average Anyway – Discusses the different “average” in calculus

Half-full and Half Empty – Average Value

Average Value Activity to help students discover the Average Value formula

Revised and updated October 22, 2018

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