Cartesian to Cyclindrical Coordinate

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destroyer130
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Problem
Printed homework problem 6: triple integral from x = -2 to 2, y from 0 to sqrt(4-x^2), z from 0 to sqrt(4-x^2-y^2), of xy dz dy dx; part (a) asks to convert to cylindrical coordinates without evaluating.

Solution answer
Triple integral written as the integral from 0 to pi of the integral from 0 to 2 of the integral from 0 to 4 minus r squared of r cubed sin(theta) cos(theta) dz dr d theta, labeled part (a).

For this one, my upper bound of z in cylindrical's is sqrt(4-r^2) instead of (4-r^2). Which one is right, mine or the solution? Thanks for helping me out.
 
destroyer130 said:
Problem
View attachment 54032
Solution answer
View attachment 54033
For this one, my upper bound of z in cylindrical's is sqrt(4-r^2) instead of (4-r^2). Which one is right, mine or the solution? Thanks for helping me out.

I'd say you are right. Must be a typo.