## Using the Mousetrap Car to Understand Calculus: Area Under the Curve (Math)

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##### Related Projects and Outlines:

In this lesson, the students will explore the area under the velocity curve to verify that this represents the distance traveled by the mousetrap car.

### Introduction

Two of the major concepts of calculus are the derivative (slope of the line tangent to a curve) and the definite integral (area under a curve between two values of the independent variable). The derivative was explored in the first lesson of this series. Now we will look at the definite integral as it relates to the velocity of the mousetrap car.

This lesson can be done whether or not the students have run their own mouse trap car activity.

### Lesson Times

Introduction to the Concepts
15 Minutes
Guided Practice
20 Minutes
Independent Practice
40 Minutes
Assessment
15 Minutes

### Industries / Subjects / Grades

##### Industries / Pathways
• Engineering & Architecture
• Engineering Design
##### K-12 Subjects
• Mathematics
• Trigonometry/Calculus
• 11
• 12

### Standards and Objectives

#### Related Instructional Objectives (SWBAT...)

• By the end of this lesson, the students understand that displacement is the area under the velocity curve and will be able to calculate this quantity using Riemann sums.

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