Areas & Volumes
In this unit scholars will begin to see the geometric applications of integrals by finding the areas between multiple curves and the x-axis and later the y-axis. Further, scholars will conceptually build upon this concept to see the relationship of area between a curve and the x-axis and the rotational solid that can be formed on either axis. From this, scholars will calculate volumes of these solids using cross sections, integration, and their calculators. Emphasis in this unit will be preparing scholars for success on the AP examination’s problems related to the topic, in particular, the free-response style problems that have occurred within the last several years.
What is the connection between integrals and areas/volumes of shapes?