Calculating Volume Using Double Integrals: Finding the Boundaries and Limits

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Homework Statement




given two surfaces S1={(x,y,z)|z=50-X^2} S2={(x,y,z)|z=9y^2+16} find the volume

1.V1 bounded above by S1 and below by S2 and on the sides by the vertical planes X=1 X=-1 Y=1 Y=-1

2 the solid V2 bounded above by S1 and below by S2 and on the sides by the vertical cylinder X^2+y^2=1

3.the solid V3 which is bounded above by the surface S1 below by S2

Homework Equations





The Attempt at a Solution



hey Please give me a help because i don't have much time !exam is today and want to understand these kind of questions !it will be nice if u can give me the steps to solve this kind of problem rather that giving answers to this questions!
 
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The exam is today and you have no idea how to even start these problems? (1), at least, is almost trivial. I would expect a problem like that to be in an earlier chapter from (2) and (3). Please try. You learn mathematics by doing mathematics, not by watching others do it.
 
ok thanks !i found the way !
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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