Volumes with infinite integrands Find the volume of the described solid of revolution or state that it does not exist.The region bounded by f(x) = (4 ? x)?1/3 and the x-axis on the interval [0, 4) is revolved about the y-axis.

Problem 39EVolumes with infinite integrands Find the volume of the described solid of revolution or state that it does not exist.The region bounded by f(x) = (4 x)1/3 and the x-axis on the interval [0, 4) is revolved about the y-axis.Answer; Step-1; The shell method ; If R is the region under the curve y = f(x) on the interval [a , b] , then the volume of the solid obtained by revolving R about the y-axis is V = 2x f(x) dx.Step-2 Now , we have to find out the volume of the described solid under the region bounded by f(x) = and the x-axis on the interval [0 , 4) is revolved about the y-axis. Consider , y = f(x) = The visual representation of the interval is given below; | | axis of revolution\n | 1\/(4 - x)^(1\/3)\n | x-axis\n(axes not equally scaled) | Therefore , the volume of the described...