Is My Disk Method Calculation Correct for Finding Volume?

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Homework Statement


Find the volume of the solid generated by revolving the shaded region about the given axis.
61prob14.jpg


Homework Equations


I used the disk method to solve this
V = int from a to b(pi * R(x)^2)


The Attempt at a Solution



V = int from 0 to 2( pi * (3Y/2)^2 dy) = 6pi
 
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TheTaoOfBill said:
Find the volume of the solid generated by revolving the shaded region about the given axis.
Which axis? It's not given.
 
Mark44 said:
Which axis? It's not given.

sorry... Over the Y axis.
 
The region is rotated around (or about) the y-axis. Yes, that's the right answer.
 

Thread 'Finding the nth roots of a complex number'

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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