Evaluate S z dS, where S is the surface whose sides S 1 are given by the cylinder x 2 y 2 1, whose bottom S 2 is the disk x 2 y 2 1 in the plane z 0, and whose top S 3 is the part of the plane z 1 x that lies above S 2

Question: Evaluate S z dS, where S is the surface whose sides S 1 are given by the cylinder x 2 + y 2 =

Evaluate ∫∫_S z dS, where S is the surface whose sides S₁ are given by the cylinder x² + y² = 1, whose bottom S₂ is the disk x² + y² ≤ 1 in the plane z = 0, and whose top S₃ is the part of the plane z = 1 + x that lies above S₂.

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