Question

Volume = ∫[0 to 1] π(2y)^2 dy 

          Volume = ∫[0 to 1] π(2y)^2 dy

Added by James M.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Volume = ∫[0 to 1] π(2y)^2 dy
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Transcript

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00:01 The region bounded by the graph of y equals x squared, shown in red, and y squared equals x, shown in blue, is rotated around the x -axis, and we're to find the volume using the washer method.
00:16 To use the washer method, our integral is going to have a pi, and then inside, we'll have the radius of the outside squared minus the radius to the inside squared.
00:29 So if we're rotating around the x -axis, we'll make a representative slice perpendicular to the axis of rotation.
00:40 So the radius to the outside would be the distance from the x -axis to the blue graph.
00:47 The blue graph is the graph of y -squared equals x.
00:51 We need the y -value...
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