Introduction to the Theorem of Pappus: The region R under the graph of y = x3 from x = 0 to x = 2 is rotated about the y-axis to form a solid (Figure 11-4p). Figure 11-4p a. Find the area of R. b. Find the volume of the solid using vertical slices of R. c. Find the first moment of area of R with respect to the y-axis. What do you notice about the integral? d. Find the x-coordinate of the centroid of R. e. A theorem of Pappus states that the volume of a solid of revolution equals the area of the region being rotated times the distance the centroid of the region travels. Show that this problem confirms the theorem

Econ 202 ~ Chapter 5 ~ Measuring A Nation’s Income The Economy’s Income and Expenditure Microeconomics is the study of how households and firms make decisions and how they interact in markets. Macroeconomics is the study of economy-wide phenomena, including inflation, unemployment and economic growth. The goal of macroeconomics is to explain the economic changes that affect many households,...