Question

Find the surface area of the part of the paraboloid z = x² * y² below the plane z = 1.

Answer 1

To find the surface area of the part of the paraboloid z = x² * y² below the plane z = 1, we integrate the area element over the region.

Step-by-step explanation:

To find the surface area of the part of the paraboloid z = x² * y² below the plane z = 1, we need to integrate the area element over the region. The area element for this surface can be expressed as dA = √(1 + (dz/dx)² + (dz/dy)²) dxdy. Since z = x² * y², we can compute dz/dx and dz/dy using partial derivatives. After integrating the area element over the region and simplifying, we get the surface area as:

A = ∬∬ √(1 + 4x²y²) dxdy