using cylindrical coordinates { ((x=rcosθ)),((y = rsin θ)),((z=z)) :} to evaluate the integral K= ∫∫∫_S (√(x^2 +y^2 −z^2 )) dxdydz where S= {(x,y,z) ∈R^3 : x^2 +y^2 ≤ 4, 0 ≤z≤(√(x^2 +y^2 ))}


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Question Number 169706 by MikeH last updated on 06/May/22
$using cylindrical coordinates { ((x=rcosθ)),((y = rsin θ)),((z=z)) :} to evaluate the integral K= ∫∫∫_S (√(x^2 +y^2 −z^2 )) dxdydz where S= {(x,y,z) ∈R^3 : x^2 +y^2 ≤ 4, 0 ≤z≤(√(x^2 +y^2 ))}$
$using cylindrical coordinates {\begin{cases} x = r \cos θ \\ y = r \sin θ \\ z = z \end{cases}$ $to evaluate the integral$ $K = \int \int \int_{S} \sqrt{x^{2} + y^{2} - z^{2}} d x d y d z$ $where$ $S = {(x, y, z) \in R^{3} : x^{2} + y^{2} ⩽ 4, 0 ⩽ z ⩽ \sqrt{x^{2} + y^{2}}}$
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