Areas

David Brown
6 min read
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Study Guide Overview
This guide covers calculating the area between two curves using definite integrals. It explains how to find the area with respect to both x and y axes. It includes steps for identifying intersection points, setting up the integral, and evaluating it. The guide provides example problems, practice questions, a glossary, and exam strategies.
#Study Notes: Area Between Two Curves
#Table of Contents
- Introduction
- Finding the Area Between Two Curves in Terms of
- Finding the Area Between Two Curves in Terms of
- Practice Questions
- Glossary
- Summary and Key Takeaways
- Exam Strategy
#Introduction
In calculus, finding the area between two curves is a common problem that requires understanding how to set up and evaluate definite integrals. This guide will help you master this topic by breaking down the steps and providing illustrative examples.
#Finding the Area Between Two Curves in Terms of
#Steps for Calculation
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Identify the Curves and Bounds:
- Consider the curves and .
- Identify the interval over which you want to find the area.
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Set Up the Integral:
- Ensure that over the interval .
- Calculate the area as:
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Evaluate the Integral:
- Compute the definite integral to find the area between the curves.
It's crucial to have the function that is "above" the other inside the integral first to ensure the integrand is always non-negative.
#Example Problem
Find the area of the region enclosed by the curves and .
- Find the Points of Intersection:
- Set the equations equal to each other and solve for : Simplify and solve...

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