# Thread: Stokes Theorem Help Needed!

1. ## Stokes Theorem Help Needed!

Use Stokes' Theorem to evaluate

$\int F \cdot dr C\ is\ oriented\ counterclockwise\ as\ viewed\ from\ above.$
$F(x,y,z) = x i + y j + (x^2 + y^2) k$
$C\ is\ the\ boundary\ of\ the\ part\ of\ the\ paraboloid\ z = 1 - x^2 - y^2 in\ the\ first\ octant\$

C is the boundary of the part of the paraboloid $z = 1-x^2-y^2$ in the first octant.

The formula for stoke's theorem is $\int F \cdot dr = \int\int curl \cdot dS$

I went ahead and found the curl which is (2y-2x)k. So, when i set up the double integral, so far i have $\int\int (2y-2x)dA$

However, im having trouble with figuring out the bounds. I think this is a sphere, so does that mean i have to use spherical coordinates? Is there a simpler way because im really not good with spherical coordinates! Thanks.

2. Sorry to bump, but i need help with this promblem within an hour! All suggestions would be appreciated .