Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Sequences and Infinite Series Power Series Vectors and Geometry of Space Vector-Valued Functions
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
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 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:

• 6.1.1 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
• 6.1.2 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
• 6.1.3 Set-up and evaluate an integral that gives the area between a negative curve and the x-axis making sign adjustments as needed
• 6.1.4 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
• 6.1.5 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

Define: area under a curve, area between two curves

Supplemental Resources (optional)