Volume of a square using cross section

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Homework Help Overview

The problem involves finding the volume of a region bounded by the curves y=x^2 and y=9, with cross sections taken perpendicular to the y-axis.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to visualize the problem through a graph and question the correct setup for the integral, particularly regarding the orientation of the cross sections.

Discussion Status

Some participants have provided guidance on visualizing the problem and clarifying the orientation of the cross sections, while others are exploring the implications of these clarifications on the integral setup.

Contextual Notes

There is a noted confusion regarding the integration variable due to the orientation of the cross sections, which may affect the approach to solving the problem.

mikaloveskero
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Homework Statement


What is the volume if the area bounded by y=x^2 and y=9 and the cross sections are perpendicular to the y axis


Homework Equations





The Attempt at a Solution


I have no idea
 
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At least draw the graph and make an attempt. Take a picture of it or scan it or just draw it in some picture editor and attach it to your post.
 
I drew the picture and y=9 is the higher graph and y=x^2 is the lower graph. So from there do you do (9-x^2)^2 and take the integral from -3 to 3 ?
 
The cross sections are perpendicular to the y-axis, not parallel. So the integral will be with respect to y, not x.
 

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