Recent content by Exus

## \iint_S (∇×\vec F)⋅\vec n \,dS = \iint_S <P, Q,\frac ∂ {∂x} (x+z) - \frac ∂ {∂y} (z-y) >⋅<0, 0, 1> \, dS = \iint_S 2\,dS = 8π ## That makes a lot of sense, thanks for the tip.

that's embarrassing, thank you. ## \vec r' (t) = <-2\sin t, 2\cos t, 0> ## ## \vec F (\vec r (t)) = <-2\sin t , 2\cos t, -\cos (2\sin t)> ## ## \int_0^{2π} <-2\sin t , 2\cos t, -\cos (2\sin t)>⋅<-2\sin t, 2\cos t, 0> \, dt = \int_0^{2π} (4\sin ^2 t +4\cos ^2 t) \, dt = 4 \int_0^{2π} \, dt = 8π ##

Homework Statement Let S be the portion of the paraboloid ##z = 4 - x^2 - y^2 ## that lies above the plane ##z = 0## and let ##\vec F = < z-y, x+z, -e^{ xyz }cos y >##. Use Stoke's Theorem to find the surface integral ##\iint_S (\nabla × \vec F) ⋅ \vec n \,dS##. Homework Equations ##\iint_S...

Closed under scalar multiplication means that any vector in the subset could be multiplied by a scalar and still be within the subset.

Consider the set of all vectors S = [x, y] such that x, y are integers. Does that work?

I'm an engineering student looking to transfer to university soon. Math and science have always been fun and I've just completed linear algebra, multi variable calculus and my first semester of E&M. Hello, and thanks in advance for all the advice, insight and help i may find here.