Question

Use cylindrical coordinates to calculate the triple integral f(xyz)dV for the given function and region:

f(xyz)=z and x^2+y^2 is less than or equal to z less than or equal to 9

Answer 1

Converting the stated bounds into cylindrical coordinates we change\[x^2+y^2\le z\le9\to r^2\le z\le9\]the region under the solid is a circle of radius 3, so the bounds are\[0\le r\le 3\]\[0\le\theta\le2\pi\]so the integral is\[\large \int_{0}^{2\pi}\int_{0}^{3}\int_{r^2}^{9}zrdzdrd\theta\]

Answer 2

@nedel please let me know if you are understanding this, communication is helpful here
welcome to Open Study :D