# Applying Stoke's Theorem to a parabaloid

1. Oct 3, 2012

### mlb2358

1. The problem statement, all variables and given/known data
Let S be the surface defined by y=10−x^2−z^2 with y≥1, oriented with rightward-pointing normal. Let F=(2xyz+5z)i+e^(x)cosyzj+(x^2)yk. Determine ∫∫∇×F·dS.

2. Relevant equations

∫∫∇×F·dS = ∫F·dS

3. The attempt at a solution
I think the boundary of the surface is the circle of radius √5 in the xz plane. The parameterization of this should be equal to <√5cost,0,√5sint>. After plugging this parameterization into F and taking the dot product with dS I got ∫-25sin2tdt from 0 to 2 pi, which equals -25∏, however this is not the correct answer. I am not sure about what I am doing wrong. I would appreciate any assistance.

2. Oct 3, 2012

### tiny-tim

hi mlb2358!

(try using the X2 button just above the Reply box )
nooo …

3. Oct 3, 2012

### HallsofIvy

Staff Emeritus
Reread your problem. What is the restriction on y?

4. Oct 3, 2012

### LCKurtz

And think about the orientation.

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