#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:

Key Concept

The area is calculated by evaluating the definite integral of a function $x = g(y)$ with respect to $y$ between $y = a$ and $y = b$ : $\int_{a}^{b} g(y) , dy$

#Steps:

Identify the function $x = g(y)$ .
Set the integration limits $y = a$ and $y = b$ .
Evaluate the definite integral: $\int_{a}^{b} g(y) , dy$ .

Exam Tip

Always ensure the function is expressed in terms of $y$ before integrating.

#Example

Given a function in terms of $x$ , $y = f(x)$ , rearrange it to $x = g(y)$ before integrating.

#Worked Example 1

#Problem:

Find the area of the region enclosed by the cur...

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Areas

David Brown