Recall: If (x, y, z) = (x(u, v), y(u, v), z(u, v)) = G(u, v) is a parametrization of the surface S with (u, v) in the parameter domain D, then [[ f(x, y, z) ds = ff f(G(u, v))||Ťu × Ťv|| du dv 1. (a) Parametrize the part S of the paraboloid z = y² + x² that lies inside the cylinder x² + y² = 9. (Hint: the graph of a function z = f(x, y) is parametrized by (x, y, z) = (x, y, f(x, y)).) (b) Find the area of the part of the paraboloid z = y² + x² that lies inside the cylinder x² + y² = 9.

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Q: D) Evaluate f (r² + y²) dady where D is the disk z² + y² ≤ 4. Usc polar coordinates. (Ans: 647/5) E)…

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Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…