Thread: Surface Integrals

Evaluate ∫∫ F dS if F(x, y, z) = xi + yj and the positive oriented surface σ is?

(a) The portion of the plane x + y + z = 1 bounded by x = 0 , y = 0 and z = 0 .

first.. z = 1 - x - y.. then, i find dz/dx = dz/dy = -1..
next, sqrt[(dz/dx)^2 + (dz/dy)^2 + 1] = sqrt3

i just don't know how to proceed with integration of xi + yj..
should i change something from this equation..?

Originally Posted by nameck

Evaluate ∫∫ F dS if F(x, y, z) = xi + yj and the positive oriented surface σ is?

Perhaps you meant $\displaystyle \vec{F}\cdot \vec{n}$ instead of $\displaystyle \vec{F}$ .