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Calculus
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9 Nov 2019

1. a. Sketch the region enclosed by the following curves.

y= (1/4) X^2 and x = (2y) ^2


b. The region defined above is revolved about the y-axis. Determinethe

volume of the resulting solid of revolution using the washer methodshowing the

integration steps.


c. Determine the volume of the same region using the method ofcylindrical

shells. Show the integration steps.

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Sixta Kovacek
Sixta KovacekLv2
30 Oct 2019

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Related questions

Use cylindrical shells to find the volume of the solid generatedwhen the region enclosed by the given curves is revolved around they-axis.

y=x^2

y=8-x^2


Please include walkthrough steps so I can learn to solve thistype of problem myself.


1. If the region above were revolved about the line y = -2, then avertical representative rectangle would generate a________ (enter Disk, Washer, or Shell). In this case, when we set up adefinite integral to find the volume of the resulting solid, thelower limit of integration would be _________ and the upper limit of integration would be _______ .

2. If the region above were revolved about the line x = 1, then ahorizontal representative rectangle would generate a_____(enterDisk, Washer, or Shell). In this case, when we set up a definiteintegral to find the volume of the resulting solid, the lower limitof integration would be _____(entera number)and the upper limit of integration would be_____ (enter a number).

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