Finding the Area Between Curves Expressed as Functions of x

Hannah Hill

5 min read

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Study Guide Overview

This study guide covers finding the area between curves expressed as functions of x. It explains how to identify the top and bottom functions, find their intersection points, and calculate the area using definite integrals. It includes a formula, walkthrough example, and a 2022 AP Calculus AB FRQ related to this topic. The importance of using a graphing calculator is also emphasized.

#8.4 Finding the Area Between Curves Expressed as Functions of x

Welcome back! On both the AB and BC exams, understanding how to evaluate the area between 1 or more functions is essential. In this topic, we will explain exactly how you find the area between two curves in terms of x so you can knock those questions out of the park. 🚀

#🔷 The Area Between Curves

When given two functions, you can determine the area between them by subtracting the integral of the bottom function ( $g(x)$ ) from the integral of the top function $(f(x))$ :

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Formula for Finding the Area Between Two Curves

Image Curtesy of Andymath

To determine the upper and lower boundaries of your definite integral, simply find what x-values the two graphs intersect at. This can be do...

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Question 1 of 10

What is the general approach to find the area between two curves, $f(x)$ and $g(x)$ , where $f(x)$ is above $g(x)$ on an interval $[a, b]$ ? 🤔

$\int_a^b [g(x) - f(x)] dx$

$\int_a^b f(x) dx + \int_a^b g(x) dx$

$\int_a^b [f(x) - g(x)] dx$

$\int_a^b |f(x) - g(x)| dx$