True or False? Justify your answers by explaining why it is true or providing a counter-example. 1. When finding the region enclosed by two curves, setting up the integrals in terms of x and in terms of y will provide the same answer. 2. The disk method can be used in any situation in which the washer method is successful at finding the volume of a solid of revolution. 3. The amount of work to pump the water out of a half-full cylinder is half the amount of work to pump the water out of the full cylinder. Solve the following problems. Show all work 4. Find the area of the region bounded by the given curves (@A) y=2022,y=2a2%-12 byy=1-2%y=1-/z Qz+y=0z=y%+3y 5. Consider the region in the first quadrant bounded by y = z* and y = 22 2. Find (a) the area of the region (b) the volume obtained by rotating the region around the w-axis (c) the volume obtained by rotating the region around the y-axis 6. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis using the disk or washer method. (@) y = 2%+ 1,y = 9 22 about the 2-axis by =22 +1,y=922about theliney = 1 7. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis using the method of cylindrical shells. 5T (@) y = cos(x),x = '2\" @ = 7, about y-axis (set up but do not evaluate) (b) y = 23,y = 8,2 = 0 about the line z = 2 True or False? Justify your answers by explaining why it is true or providing a counter-example. 1. When finding the region enclosed by two curves, setting up the integrals in terms of x and in terms of y will provide the same answer. 2. The disk method can be used in any situation in which the washer method is successful at finding the volume of a solid of revolution. 3. The amount of work to pump the water out of a half-full cylinder is half the amount of work to pump the water out of the full cylinder. Solve the following problems. Show all work 4. Find the area of the region bounded by the given curves (@A) y=2022,y=2a2%-12 byy=1-2%y=1-/z Qz+y=0z=y%+3y 5. Consider the region in the first quadrant bounded by y = z* and y = 22 2. Find (a) the area of the region (b) the volume obtained by rotating the region around the w-axis (c) the volume obtained by rotating the region around the y-axis 6. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis using the disk or washer method. (@) y = 2%+ 1,y = 9 22 about the 2-axis by =22 +1,y=922about theliney = 1 7. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis using the method of cylindrical shells. 5T (@) y = cos(x),x = '2\" @ = 7, about y-axis (set up but do not evaluate) (b) y = 23,y = 8,2 = 0 about the line z = 2