Section 7 1 Area of a Region Between

Section 7. 1 Area of a Region Between Two Curves AP Calculus BC

Learning Targets Find the area between two curves using a vertical cross section Find the area between two intersecting curves Find the area between two curves using a horizontal cross section

Exploration

Area Between Two Curves Formula

Example 1

Example 2

Example 3: Intersecting Curves

Example 4: Intersecting Curves

Example 5: What about the graphs…

Example 1: More than 2 Intersections

Example 2: More than 2 Intersections

Example 4: Sub Regions

Integrating with Respect to y Sometimes one option for finding the area between two curves is to tilt your head and visualize the graphs with respect to the y-axis. In some cases, integrating with respect to y can be a much more efficient process than splitting a region up in to two areas. **We often call this process “Horizontal Cross Sections”** When integrating with respect to the y-axis, be sure to: 1. Isolate x in any functions that are boundaries of the region 2. Use limits of integration that are y-values.

Example 5: Horizontal Cross Sections

Example 6: Horizontal Cross Sections

The Integral as an Accumulator Function AP really emphasizes the integral as an accumulator function. Read Example 6 on p. 441 that really does a nice job explaining it.

Exit Ticket

Exit Ticket – Answer #1

Exit Ticket – Answer #2

Exit Ticket – Answer #2

Exit Ticket – Answer #3