Find the volume of the solid obtained by rotating the region

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Homework Help Overview

The discussion revolves around finding the volume of a solid obtained by rotating a region bounded by the curves y=1-x² and y=0 about the x-axis. Participants are engaged in visualizing the problem through sketches and exploring the concept of solids of revolution.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss their sketches of the region and the solid, with one seeking confirmation on their understanding of the typical disk or washer method. Another participant questions the location of the solid in relation to the function.

Discussion Status

The discussion is active, with participants sharing sketches and expressing their thoughts on the problem. Some guidance has been offered, but there is no explicit consensus on the approach or solution yet.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can share or the methods they can use.

phillyolly
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Homework Statement


Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. About x axis.
1)
y=1-x2
y=0

Homework Equations


The Attempt at a Solution



I sketched a curve and a region. A typical disk and a solid? And please check the solution?
 

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Everything looks good. Good job!
 
I drew a little sketch to give you some extra intuition on solids of revolution.

See figure.
 

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That's great, thank you! I will try now to solve both of the problems. Let's see what happens.
 
Hey, where is the solid located on the function?
 

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