Math Problem Solver

Evaluate the surface integral

S

F · dS

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = xz i + x j + y k,

S is the hemisphere

x^2 + y^2 + z^2 = 25, y ≥ 0,

oriented in the direction of the positive y-axis