I) Sketch the curve defined by y = e^x from x = 0 to x = 2. If this curve is rotated about the y-axis, set up the following integrals (hint: use yor calculator to check that you get the same result from bothntegrals):

a) make a dx integral for the surface area of this surface of revolution

b) make a dy integral for the surface area of this surface of revolution.

II) Sketch the region bound by the curves y = sin x and the x-axis from x = 0 to x = (pie) Find the exact coordinates of the center of mass of this region given a uniform density. Do not approximate your result, and show all work for your integration.