Q4 Cal 2

4. The diagram at the right shows a "profile region" for generating solids of revolution. The quarter-circle is P.R. part of the unit circle, x+ y' =1, which implies then that the two line segments are parts of the straight lines x =1 and y =1. A. Find the area of the profile region. It should not be necessary to use an integral; you should be able to figure it out geometrically. B. Set up the y-integral for the solid obtained by revolving the profile region about the y axis. C. Set up the x-integral for the same solid you worked with in part B. D Find the volume of the solid used in parts B and C. You may use either of the integrals you obtained in parts B and C, or you can figure it out geometrically. E Set up and calculate the solid obtained by revolving the profile region about the upper boundary, y =1. In this example I doubt you can find a purely geometric way to do it