The density of a solid cylinder defined by the equation y² + z² ≤ a² and 0 ≤ x ≤ b is proportional to the distance from the x-axis, expressed as k√(y² + z²). The discussion clarifies that the density can be represented in polar coordinates as f(x, r, θ), where r is the radius given by r = √(y² + z²). The integral for calculating the mass of the cylinder with a radius of 6 and length of 11 is set up as ∫₀¹¹∫₀²π∫₀⁶ kr² dr dθ dz.
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