Question

6. Consider the graph of the curve y = (a) Find the area under the curve from :=1 to r= 100. (b) What happens to the area under the curve as the right hand endpoint goes to co? (c) Find the volume of the solid obtained by rotating this curve around the c-axis from x=1 to r= 100. (d) What happens to the volume in part (c) as the right hand endpoint goes to co? (e) Find the volume of the solid whose base is this region bounded by the curves y = 1/2, y=0, x= 1 and 2 = 100 and whose cross-sections perpendicular to the z-axis are right triangles whose height is half their base. (f) What happens to the volume in part (e) as the right hand endpoint goes to co?