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## Homework Statement

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Consider

**F**= (y - z)

**i**+ (z - x)

**j**+ (x + z)

**k**

Find circulation of

**F**in the clockwise direction as seen from above, around the boundary of surface S defined by

z = 4 - x

^{2}- y

^{2}

0 ≤ z ≤ 4

## Homework Equations

∫∫ ∇x

**F**•

**k**dA

## The Attempt at a Solution

∇x

**F**=

**i**- 2

**j**- 2

**k**(after solving the cross product)

The curl of

**F**dot

**k**= -2

0 ≤ r ≤ 2

0 ≤ θ ≤ 2π

∫∫ -2 drdθ = ∫ -4 dθ =

__-8π__-8π is the counterclockwise circulation of

**F**, but since the problem asks for the clockwise direction, would the answer just be 8π (opposite sign)?