2 min readβ’june 8, 2020

Anusha Tekumulla

This is one of the most important topics of Unit 8. In this topic, we will discuss how to **find the area between two curves expressed as functions of x.** This topic will set you up to understand more complex topics moving forward. To understand how to find the area, take a look at this simple example:Β

Letβs say we want to find the area between the curve y = x and y = x^2 from x = 2 to x = 4. In order to find the area, you can **imagine we are slicing the region vertically**, into a bunch of infinitely thin slices. The area would be the **sum of all the slices**. To add all the slices, you can use a definite integral. Integrate the function (x^2 - x) from 2 to 4.Β

Hereβs a basic formula to understand the concept:Β

Also, it is important to mention that you can only **use **this specific method **when your functions are expressed in terms of x.** In the example above, our functions were x and x^2. If the functions were y and y^2, we would have to use a slightly different approach. To learn more, look at Topic 8.5: Finding the Area Between Curves Expressed as Functions of y.Β Β

If youβre still confused, try out this example and see how you do.Β

Solution: First, we should set the functions equal to each other to find the intersection points. If you do x^2 - 2 = -x^2 and solve for x, you should get x = -1 and x = 1. Next, graph the functions to figure out which one is on top. You should get something like this:

Sign up now for instant access to 2 amazing downloads to help you get a 5

Browse Study Guides By Unit

π

Big Reviews: Finals & Exam Prep

βοΈ

Free Response Questions (FRQ)

π§

Multiple Choice Questions (MCQ)

βΎ

Unit 10: Infinite Sequences and Series (BC Only)

π

Unit 1: Limits & Continuity

π€

Unit 2: Differentiation: Definition & Fundamental Properties

π€π½

Unit 3: Differentiation: Composite, Implicit & Inverse Functions

π

Unit 4: Contextual Applications of the Differentiation

β¨

Unit 5: Analytical Applications of Differentiation

π₯

Unit 6: Integration and Accumulation of Change

π

Unit 7: Differential Equations

πΆ

Unit 8: Applications of Integration

π¦

Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)

Thousands of students are studying with us for the AP Calculus AB/BC exam.

join nowPractice your typing skills while reading Finding the Area Between Curves Expressed as Functions of x

Start GameTake this quiz for a progress check on what youβve learned this year and get a personalized study plan to grab that 5!

START QUIZTake this quiz for a progress check on what youβve learned this year and get a personalized study plan to grab that 5!

START QUIZStudying with Hours = the ultimate focus mode

Start a free study session