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Calculus II
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Calculus III

Course: Calculus II
Topic: Geometry
Subtopic: Area Between Two Curves

Overview

One useful application of calculus is in the area of geometry. In this lesson we find the area of an irregular shape such as that formed between two (or more) intersecting curves. The plan is to slice the region into thin parallel strips then use definite integrals to sum-up all the strip areas to get the area of the entire shape.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 6.2.1 Set-up and evaluate an integral that gives the area under a positive curve, i.e. the area between the curve and the x-axis
• 6.2.2 Understand that curves that lie below the x-axis have positive area although the integral, depending how it is set-up, may give a negative answer and how to adjust for that sign dilemma
• 6.2.3 Set-up and evaluate an integral that gives the area between a negative curve and the x-axis making sign adjustments as needed
• 6.2.4 Set-up and evaluate an integral that gives the area between a curve and the x-axis when the curve crosses the x-axis on the interval of integration
• 6.2.5 Set-up and evaluate an integral that gives the area between two curves including those that intersect each other on the interval of integration

Terminology

Terms you should be able to define: area under a curve, area between two curves

Mini-Lectures and Examples

Supplemental Resources (optional)

PDF: First Applications of Definite Integrals, Dale Hoffman's Contemporary Calculus I (beginning pages, "Area Between f and g" section)

rev. 2021-01-03