Volume of a solid in first quadrant

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Homework Help Overview

The problem involves finding the volume of a solid whose base is defined by the region in the first quadrant, bounded by the curves y=x^2 and y=x. The solid has square cross sections perpendicular to the x-axis.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to visualize the problem through sketches and question which equations or setups are appropriate for calculating the volume.

Discussion Status

Some participants have provided guidance on visualizing the solid and identifying the volume element, while others express uncertainty about the equations and setup needed for the calculation. Multiple interpretations of the approach are being explored.

Contextual Notes

Participants are navigating the boundaries defined by the curves and the intersection points, which are crucial for setting up the integration limits.

Ashford
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Homework Statement


Find the volume of the solid whose base is the region in the first quadrant bounded by the curves y=x^2 and y=x, and whose cross sections perpendicular to the x-axis are squares.



No idea what to do here
 
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Start by drawing a graph of the region. Then draw a sketch of the solid object.
 
Ok, I've done that but I still don't know which equation to use and how to set it up.
 
Your typical volume element has a base that extends from y = x^2 up to y = x, has the same height, and is [itex]\Delta x[/itex] wide. Your limits of integration are the values of x where the two curves intersect.
 

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