Thread: surface integrals

Consider the hemispherical volume V defined by:
x^2 + y^2 + z^2 =< a^2, z>=0, and denote its closed surface by S.
Define the vector field f=(-y, x, z^2)

a) Evaluate the net outward flux of f through S by direct integration.

{to parameterise the curved surface use spherical polar coordinates}

plz help me its due in a few hours

Originally Posted by martinr

Consider the hemispherical volume V defined by:
x^2 + y^2 + z^2 =< a^2, z>=0, and denote its closed surface by S.
Define the vector field f=(-y, x, z^2)

a) Evaluate the net outward flux of f through S by direct integration.

{to parameterise the curved surface use spherical polar coordinates}

plz help me its due in a few hours

The vector-function defined by where will parametrize the upper hemi-sphere.

Then, .
Where depends whether the parametrization was inward or outward. Just pick a vector and check which was it goes.