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K Determine whether the following statements are true and give an explanation or counterexample a When using the shell method the axis of the cylindrical shells is parallel to the axis of revolution b If a region is revolved about the y axis then the shell method must be used c If a region is revolved about the x axis then in principle it is possible to use the disk washer method and integrate with respect to x or the shell method and integrate with respect to y GEXEND CC True The rotation of the function about the axis creates a cylindrical shape parallel to the axis OD False The rotation of the function about the axis creates a disk shape perpendicular to the axis b Choose the correct answer below A True Any time a function is revolved about an axis the shell method must be used OB False The shell method can only be used when a region is revolved about the x axis OC True Then the axis of the cylindrical shells is parallel to the y ixis D False The disk washer method may be used by integration with respect to y c Choose the correct answer below OA True If the disks washers are perpendicular to the axis of revolution x must be used and if the shells are parallel to the axis of revolution y must be used OB False Use the disk washer method and integrate with respect to y or the shell method and integrate with respect to x C True Integration must always to with respect to the parallel variable be used when revolved about the x axis

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