Surface integrals using a parametric description. evaluate the surface integral \int \int_{s} f(x, y,z)ds using a parametric description of the surface.

f(x, y,z)=x2+y2, where s is the hemisphere x2+y2+z2=36, for z> =0

You can parameterize using spherical coordinates by

with and .

Take the normal vector to to be

(I use to avoid negative signs. The orientation of the normal vector doesn't matter for a scalar surface integral; you could just as easily use .)

Then

and the integral of over is

no one knows lol

step-by-step explanation:

5/12, or 5: 12

step-by-step explanation: