Quick cal question (probably simple

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SUMMARY

The discussion focuses on calculating the volume of a solid with a base defined by the curves y=x^2 and y=x, using square cross-sections perpendicular to the x-axis. The correct setup for the integral involves determining the side length of the square, which is the difference between the two functions, specifically (x - x^2). The volume is then calculated by integrating the area of the squares from x=0 to x=1, leading to the integral of (x - x^2)^2 dx over the specified interval.

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Homework Statement


The base of a soild is the region bounded by y=x^2 and y=x. Find the volume if cross sections perpendicular to the x-axis are squares


Homework Equations


Integral of A(x)dx


The Attempt at a Solution



Ok, so I have to take the integral from 0 to 1 after solving for X

since it is a square, the setup is side^2dx... For some reason i cannot figure out the value used for side using 2 functions...

I believe it should be something similar to 2(side)^2dx evaluating from 0 to 1, but what is the value for side and how was it found?
 
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y=x^2 is below y=x between x=0 and x=1. So isn't 'side' x-x^2, the distance between them??
 

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