CAN SOMEONE HELP ME IN THIS INTEGRAL QUESTION PLS ''Find the surface area between the z = 1 and z = 4 planes of z = x ^ 2 + y ^ 2 paraboloid.''

Due to the symmetry of the paraboloid about the z-axis, you can treat this is a surface of revolution. Consider the curve , with , and revolve it about the y-axis. The area of the resulting surface is then

But perhaps you'd like the surface integral treatment. Parameterize the surface by

with and , where the third component follows from

Take the normal vector to the surface to be

The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:

Then the area of the surface is

which reduces to the integral used in the surface-of-revolution setup.

oof cheaters cheat because they’re lazy that’s why i cheat xd

: )

step-by-step explanation: