How to Find the Area Between Two Curves

This lesson explains how to find the area between two graphs using definite integrals with respect to the x-axis.

Summary

The video will show you how to identify top and bottom functions, set correct limits of integration, and handle cases where graphs intersect or cross the x-axis. The video emphasizes using “top minus bottom” and shows how to split integrals when necessary. Several examples demonstrate both exact answers and calculator/Desoms-based solutions, including the use of absolute value to simplify area calculations. This skill is essential for solving free-response questions and understanding geometric meaning in integral calculus.

Key Takeaways

• Area between two curves is found using a definite integral of top function minus bottom function.

• The formula works regardless of whether the region is above or below the x-axis.

• If limits of integration are not given, they must be found by solving where the functions intersect.

• When the top and bottom functions switch, the integral must be split into multiple parts.

• Area is always positive, even when the definite integral itself would be negative.

• Absolute value can be used to compute total area in one integral when using technology.

• On free-response questions, students must show setup, limits, and correct integrand.

Transcript

All right everyone, Mr. Antonucci here. In this video we’re going to talk about area between graphs, particularly how to find the area between two functions with respect to the x-axis.