Convert the integral from rectangular coordinates to both cylindrical and spherical c

[nikkilooloo]

Convert the integral from rectangular coordinates to both cylindrical and spherical coordinates, and evaluate the simplest integral.

∫∫∫ xdzdydx
first integral is from -9 to 9
second integral is from -√(81-x^2) to √(81-x^2)
third integral is from x^2 + y^2 to 81

the integrals in spherical coordinates needs to be broken into two parts and added together. I can't really wrap my head around how to do this, every time I think I get it, it's marked wrong. Thanks for any help in advance!


So far I have

cylindrical:

∫(0 to 2π) ∫ (0 to 9 ∫ (r^2 to 81) dz dr dtheta

I don't know what to put for x in cylindrical coordinates?


spherical:

∫(0 to 2π) ∫ (0 to arctan(1/9) ∫(0 to 9) (not sure what to put here in place of x) d roe d phi d theta

+ ∫(0 to 2π) ∫(arctan(1/9 ) to something?) ∫(0 to something) (not sure what to put here in place of x) d roe d phi d theta