Area Between Two Curves with Respect to y

This lesson explains how to find the area of regions bounded by curves with respect to the y-axis using definite integrals.

Summary

The video will show you how to set up integrals in terms of y, using “right minus left” instead of “top minus bottom,” finding intersection points, and rewriting equations in terms of x. Examples include regions that can be solved both with respect to x and with respect to y, helping you decide which method is easier and why this skill is important for AP Calculus problems.

Key Takeaways

• Sometimes regions cannot be found using vertical rectangles and must be partitioned with respect to the y-axis.

• When integrating with respect to y, the area formula is right boundary minus left boundary.

• The integral for area with respect to y is written from y = c to y = d and uses dy.

• Intersection points are found by setting the equations equal and solving for y.

• All equations must be rewritten in terms of x before setting up a dy integral.

• Some regions can be solved with respect to either x or y, but one method is often simpler.

• The area result is the same regardless of whether you integrate with respect to x or y.

Transcript

All right everyone, Mr. Antonucci here. Continuing on with Section 2 of Chapter 8, we’re going to talk about what happens when you find area with respect to the y-axis.