Quick cal question (probably simple

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In summary, the problem asks to find the volume of a solid with a base bounded by the functions y=x^2 and y=x, and cross sections perpendicular to the x-axis being squares. To solve this, we need to take the integral of the area function A(x) from 0 to 1, where A(x)=side^2dx. The value for side can be found by subtracting the functions y=x and y=x^2, giving us a distance of x-x^2. This value can then be used to evaluate the integral from 0 to 1 and find the volume of the solid.
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r6mikey
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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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  • #2
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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