Area between curves

Learning objectives

Set up and evaluate a definite integral for the area between two curves expressed as functions of x, integrating the upper curve minus the lower curve

Set up and evaluate the area between curves expressed as functions of y, integrating the right curve minus the left curve over an interval of y

Find the area of a region bounded by curves that intersect at more than two points by splitting the integral at the intersection points where the curves swap position

Find the intersection points of curves with a graphing calculator, keep them to full precision and use them as limits of integration in calculator-active questions

Choose between integrating with respect to x or with respect to y to describe a region with a single integral, and find the line that divides a region into two parts of equal area