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Question Number 169706 by MikeH last updated on 06/May/22

using cylindrical coordinates {\begin{cases} x = r \cos θ \\ y = r \sin θ \\ z = z \end{cases}

to evaluate the integral

K = \int \int \int_{S} \sqrt{x^{2} + y^{2} - z^{2}} d x d y d z

where

S = {(x, y, z) \in R^{3} : x^{2} + y^{2} ⩽ 4, 0 ⩽ z ⩽ \sqrt{x^{2} + y^{2}}}