?Let Q be the solid bounded by the xy-plane, the cylinder \(x^{2}+y^{2}=a^{2}\) , and

Chapter 5, Problem 351

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Let Q be the solid bounded by the xy-plane, the cylinder \(x^{2}+y^{2}=a^{2}\) , and the plane z = 1, where a > 1 is a real number. Find the moment \(M_{x y}\) of the solid about the xy-plane if its density given in cylindrical coordinates is \(\rho(r, \theta, z)=\frac{d^{2} f}{d r^{2}}(r)\), where f is a differentiable function with the first and second derivatives continuous and differentiable on (0, a).

Text Transcription:

x^2 + y^2 = a^2

M_xy

rho(r, theta, z) = d^2 f/dr^2 (r)