So I am looking to solve the triple integral using cylindrical coordinates. I believe this is quite simple however I am getting my bounds of integration confused.
The triple integral x^2+y^2+z^2 is defined by x^2+y^2<=1 and |z|<=1.
From this i have drawn up my cylinder and determined that the radius is 1 centred about the origin with the z axis ranging from -1
Now setting up the triple intergral is where I am getting confused also.
I know x=rcos(theta), y=rsin(theta) and z=z.
From here I am unsure how to proceed in setting up the triple integral. I think my understanding about how to incorporate the correct set up into the cylindrical coordinate system is what's making me lack.
HINT
The set up is
$$\int_0^{2\pi}d\theta \int_{-1}^1 dz \int_{0}^1 f(r,\theta,z)\,r\,dr$$