Answer: 451 **Region R is bounded by y = x, the x-axis # and the line x = 2. Region R is rotated about the line y = -3 Answer: 1287 ** Region R is the area between y = x and y = 4x - x? in the first quadrant. Region R is rotated about x-axis. 4X - x² = x² x =0, x =2 1x² + 3)² 97 ds -x ) dx V = 1127 64T Tz X 3 LxT LYS 112 Answer: Answer: 2401 Region R is bounded by y = xạ, the x-axis ** Region R is the area between y = x? and and the line x = 2. Region R is rotated about y = 4x - x? in the first quadrant. Region R the line x = -2. is rotated about the line y = 6. 2T x² = 44-x² (X+2 x 2d - x² + 4x=0 X(4-x)=0 x=0, x=4 Ta (6 - x² ) -(6-4x+x) dx wlot 64 Answer: 1447 # 11 **Region R is bounded by the lines + 3, the y-axis and the x-axis. Region R is rotated about the y-axis. 2x +3=0 Answer: 967 Region R is bounded by the lines -x + 3, the y-axis and the x-axis. Region R is rotated about the x-axis. OR