Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z) = x2 + y2

The surface element is

and the integral is

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To compute the last integral, you can integrate by parts:

For this integral, consider a substitution of

and the result above follows.

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step-by-step explanation: