Volume of a square using cross section

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To find the volume of the area bounded by y=x^2 and y=9 with cross sections perpendicular to the y-axis, first sketch the graphs to visualize the region. The correct approach involves using the formula for the area of the cross section, which is (9 - y)², and integrating with respect to y. The integration limits should be from 0 to 9, as these represent the y-values where the curves intersect. The integral will yield the volume of the solid formed by these cross sections. Understanding the orientation of the cross sections is crucial for setting up the integral correctly.
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


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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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