compute surface areas by using surface integrals for the following surfaces: (i) z = x^2 + y^2, z = - (x^2 + y^2)
Question
Solution 1
To compute the surface area using surface integrals, we first need to parameterize the surface.
(i) For the surface z = x^2 + y^2, we can use cylindrical coordinates (r, θ, z) where x = rcos(θ), y = rsin(θ), and z = r^2. The differential area element in cylindrical coordinates is dS = rdθdz.
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