Areas

David Brown
6 min read
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Study Guide Overview
This study guide covers calculating the area between a curve and the y-axis using definite integrals. It explains how to set up the integral with the function expressed in terms of y, determine the limits of integration, and handle cases with no given limits or negative area integrals. The guide also includes worked examples and practice questions.
#Study Notes: Area Between a Curve and the Y-Axis
#Table of Contents
- Introduction
- Finding the Area Between a Curve and the Y-Axis
- Worked Example 1
- No Given Limits
- Negative Area Integrals
- Worked Example 2
- Practice Questions
- Glossary
- Summary and Key Takeaways
#Introduction
This section covers the method to find the area between a curve and the y-axis using definite integrals. Understanding this concept is essential for solving problems related to areas under curves in coordinate geometry.
#Finding the Area Between a Curve and the Y-Axis
To find the area between a curve and the y-axis, follow these steps:
The area is calculated by evaluating the definite integral of a function with respect to between and :
#Steps:
- Identify the function .
- Set the integration limits and .
- Evaluate the definite integral: .
Always ensure the function is expressed in terms of before integrating.
#Example
Given a function in terms of , , rearrange it to before integrating.
#Worked Example 1
#Problem:
Find the area of the region enclosed by the cur...

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