How to find the new limits of integration

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SUMMARY

The discussion focuses on determining the new limits of integration when using the washer method to rotate the function y = 9 - x² about the x-axis. The user correctly identifies that to find the new limits, one must solve for y when given specific x values, specifically at x = 0 and x = 3. The new limits of integration are thus y = 9 and y = 0, respectively. The user also inquires whether new limits are necessary for the disk and shell methods, which is confirmed to be applicable primarily to the washer and shell methods.

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Homework Statement



I'm confused about a certain aspect of shell method, washer method, and disk method. If I want to rotate using the washer method about the x-axis how do I get the new limits of integration?

For example: y = 9-x2 over [0,3] about x-axis.
I solved for x and got: x = sqrt(9-y) but how do I calculate the new limits?
Also do I need to find the new limits for disk, shell, and washer method in certain cases or is it only for shell and washer?

I know how to set up and solve the integral it's just calculating the new limits. Any help would be great.
 
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You are initially given values for x, so when x=0 what is y? Similarly when x=3 what is y?

(from the equation y=9-x2)

Those will be your limits.
 

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