Assessment item #1

Use the graphs below to answer the questions. Slide point D along the curve to see the solid generated by the rotation of the graphed region about the x-axis. Points A, B, and C are the intersections of the graphed equations.

What is the equation whose rotation creates the solid? About which axis is it rotated? What is the lower limit of the region? What is the upper limit of the region? Write an expression for the radius of the region. Write an expression for the area of a cross section of the region. What variable is used in the integration to calculate the volume? Create an integral using the area expression, lower limit, and upper limit to calculate the volume of the solid. Evaluate the integral using the appropriate technique.