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For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the y-axis. 82.
For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the y-axis. 82. y = 4 x, x = 0, and y = 0 83. y=2x3, x = 0, x = 1, and y = 0 84. y = 3x2, x = 0, and y = 3 85. y=4x2, y = 0, and x = 0 86. y= x+1 x = 0, and x = 3 87. x = sec (y) and y = 1,y= 0 and x = 0 88. y=1, x = 0, and x = 2 - 89. y = 4 x, y = x, and x = 0
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