Find the surface area of the part of the paraboloid z=5-3x^2-2y^2 located above the xy plane. (10 points) z

Use the formula

Step-by-step explanation:

Let be the explicit parametrization of the paraboid. The intersection of this paraboid with the xy plane is the ellipse given by

The partial derivatives of the parametrization are:

and computing the cross product we have

. Then

Then,  if is the interior region of the ellipse the superficial area located above of the xy  is given by the double integral

The last integral is not easy to calculate because it is an elliptic integral, but with any software of mathematics you can obtain this value.

it is probably the graph on the bottom right.

23

step-by-step explanation: