Find the volume of the solid of revolution generated by revolving about the x-axis the region under the following curve. y= vx from x =0 to x = 18 (The solid generated is called a paraboloid.) The volume of a solid of revolution obtained from revolving the region below the graph of y = g(x) from x = a to x = b about the x-axis is mig(x)]?dx. a First, rewrite the equation and perform the substitutions y = g(x) from x = a to x = b. 18 [La( x ) ] ox = ] x (Vx) ? dx a Simplify the integrand. 18 18 It ( Vx) 2dx = xx dx 0 ntegrate with respect to x. 18 18 TX dx = Evaluate the result over the limits of integration. 18 2 = 162x Therefore, the volume of the solid of revolution is 162x