Need help setting up integral. (Doesn't have to be solved)

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Homework Help Overview

The problem involves setting up a definite integral to find the volume of a solid formed by revolving a region enclosed by the curves y=(x^2)-1, x=2, and y=0 around the y-axis.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss their attempts to graph the region and express uncertainty about the correct integral setup. Questions arise regarding the choice between using shells or disks for volume calculation.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the setup of the integral. Some guidance is offered regarding the visualization of the revolved solid, but no consensus has been reached on the correct approach.

Contextual Notes

Participants are working under the constraint of needing to set up the integral without solving it, which may limit their exploration of the problem.

Ashford
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Homework Statement


Set up a definite integral that could be evaluated to find the volume of the solid that results when the region enclosed by the curves y=(x^2)-1, x=2, and y=0 is revolved about the y-axis.
(doesn't have to be solved) I have look at my book for help and I'm stuck.
 
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What have you tried so far?

Please post your attempt and any rough work that pertains to this problem.
 
I've graphed it, but that still doesn't get me any where I don't know which integral to set it up with.
 
Ok this is what i got probably wrong. V=\pi (integral) [x2-1] dy

with the lower limit of the integral being 0 and the top being 2
 
What does the region that will be revolved around the y-axis look like? Have you drawn a sketch of the revolved solid. Are you going to use shells or disks to get the volume?

What expression represents your typical volume element?
 

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