7.2 Areas in the Plane (areas between two functions) Objective: SWBAT use integration to calculate areas of regions in a plane.

Let’s review the concept of area as it relates to calculus!!! This lesson does the same thing, except the area won’t be between the curve and the x- axis, but rather between two curves.

Example 1: Draw a rectangle between the two curves. a) What is the height and width of the rectangle? b) Would the height and width of the rectangle be different if you drew it in a different place? Nope!

Example 2: The area under the curve is approximately the sum of all those rectangles. We can write this as: Example 3: How can we get closer to the ACTUAL area between the curves? Example 4: If we let the number of rectangles approach infinity, we have: Make more rectangles!!! (head to infinity…and beyond)

To begin this process, draw a graph and shade your desired region. Next, draw a rectangle to help you set up your integral. Then solve the integral to find the area.

We can’t use vertical rectangles. We have to use horizontal ones. We have to integrate with respect to y. For your limits, look at the lowest value y can be and the highest value y can be.