zuai-logo

Areas

David Brown

David Brown

6 min read

Listen to this study note

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

  1. Introduction
  2. Finding the Area Between a Curve and the Y-Axis
  3. Worked Example 1
  4. No Given Limits
  5. Negative Area Integrals
  6. Worked Example 2
  7. Practice Questions
  8. Glossary
  9. 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)x = g(y) with respect to yy between y=ay = a and y=by = b: abg(y),dy\int_{a}^{b} g(y) , dy

Steps:

  1. Identify the function x=g(y)x = g(y).
  2. Set the integration limits y=ay = a and y=by = b.
  3. Evaluate the definite integral: abg(y),dy\int_{a}^{b} g(y) , dy.
Exam Tip

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

Example

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

Worked Example 1

Problem:

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

Question 1 of 9

Ready to find some areas? 📐 What is the area between the curve x=yx = y and the y-axis from y=1y = 1 to y=3y = 3?

2

4

6

8