Triple Integral Help: Find Mass in Cylindrical Coords

[bdario1]

Find the mass of the region (in cylindrical coordinates)r^3<=z<=1 , where the density function is r(r;q; z) = 9z.

This is what I got so far

0 <= r<= 1; 0 <= q <= 2p:
hence need to compute the integral
Z from 0 to 2pi Z from 0 to 1 Z r^3 to 1 9zdzrdrdq:
We thus obtain
9p Z 0 to 1(1^2-r^6) r dr


Now this is where I am not able to get to the answer not sure why.

 

[tiny-tim]

welcome to pf!

hi bdario1! welcome to pf!

(hav an integral: ∫ and a theta: θ and a pi: π and try using the X² icon just above the Reply box )

Find the mass of the region (in cylindrical coordinates)r^3<=z<=1 , where the density function is r(r;q; z) = 9z.

This is what I got so far

0 <= r<= 1; 0 <= q <= 2p:
hence need to compute the integral
Z from 0 to 2pi Z from 0 to 1 Z r^3 to 1 9zdzrdrdq:
We thus obtain
9p Z 0 to 1(1^2-r^6) r dr


Now this is where I am not able to get to the answer not sure why.

looks ok to me (though not very readable) …

what is the answer?​

 

[totally_lost]

I think you should obtain Pi/4 9^3 as answer. Please be more careful when formulating your problem, because it not very readable indeed.