Chapter 5, Problem 442RE

The following problems concern the Theorem of Pappus (see Moments and Centers of Mass (http:Ilcnx.orgl contentlm53649llatestl) for a refresher), a method for calculating volume using centroids. Assuming a region R, when you revolve around the x-axis the volume is given by $V_x=2\pi A\bar{y}$ . and when you revolve around the y-axis the volume is given by $V_y=2\pi Ax$. where A is the area of R. Consider the legion bounded by $x^2+y^2=1$ and above $y=x+1$ .

442. Find the volume when you revolve the region around the y-axis.