A solid is obtained by rotating the shaded region about the specified line. about the x-axis y V = 3 2 1 y=x 2 4 2 y = 6 - x 6 8 (a) Set up an integral using the method of cylindrical shells for the volume of the solid. [] dy 10 (b) Evaluate the integral to find the volume of the solid. X Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 6x - x, y = x; about x 7 dx Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. 12 + x, y=0, x = 0, x= 2 y = Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. y = x, x= 0, y = 5 Consider the following. y = 5xex, y = 0, x = 3; about the y-axis (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. dx (b) Use technology to evaluate the integral. (Round your answer to five decimal places.) A solid is obtained by rotating the shaded region about the specified line. about the line y = 4 y x = 4y - y 3 X = 3 (a) Set up an integral to find the volume of the solid. dy (b) Evaluate the integral to find the volume of the solid. Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. Sketch the solid. y=6 sin(3 x) h(x) = Graph XXXXXXX V 3 Graph Description What are the circumference c and height h of a typical cylindrical shell? c(x) = Use the method of cylindrical shells to find the volume V of S. Graph Graph Description 3/001/XXX/XX=30/1|||||||||| -1.5 -1 -0.5 -0.5 1 1.5 Graph Graph Description -1.5 -1 -0.5 -0.5 Graph -1 Graph Description What are the circumference c and height h of a typical cylindrical shell? c(x) = h(x) = Use the method of cylindrical shells to find the volume V of S. Do you think this method is preferable to using washers? Explain your reasoning.