# Boundaries of $\iiint\limits_V \sqrt{x^2+y^2} \,\mathrm dx\,\mathrm dy \,\mathrm dz$

How to find out boundaries of triple integrals ? How to switch paraboloid in equation into other coordinates. I've tried to switch into spherical coordinates, but it didn't help, since in the end i couldn't find theta boundaries. The integral is given below:

$$\iiint\limits_V \sqrt{x^2+y^2} \,\mathrm dx\,\mathrm dy \,\mathrm dz$$

$$\bar V = \{ (x,y,z)\in \mathbb R : z\leq 5- x^2 -y^2, 2z \geq \sqrt {x^2 + y^2},y \geq0\}$$

• Those boundaries are made for cylindrical coordinates. – Brian M. Scott May 22 at 23:36
• how would u implement those ? – paweta May 22 at 23:39
• ok i got it, thanks for hint :) – paweta May 22 at 23:51
• You’re welcome! – Brian M. Scott May 22 at 23:52