Lesson: Area between a Curve and a Line Mathematics • Higher Education

In this lesson, we will learn how to apply integration to find the area between the curve of a function and a horizontal or vertical straight line.

Lesson Plan

Students will be able to

use definite integrals to find the area between the curve of a given function and any horizontal line of the form ,
use definite integrals to find the area between the curve of a given function and any vertical line of the form ,
use definite integrals to find the area between the curve of a given function and a line, where the area is represented graphically.

Lesson Video

Lesson Explainer

Sample Question Videos

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Lesson Worksheet

Q1:

The curve shown is . What is the area of the shaded region? Give an exact answer.

Q2:

A glassed, arched entry to a hotel follows the curve , where is the vertical height of the arch at a horizontal distance of meters from a point on the floor. If glass costs 1,190 LE per square meter, calculate the cost of the entrance.

Q3:

The curve shown is . What is the area of the shaded region? Give an exact answer.