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## Homework Statement

verify Stokes theorem for the given Surface and VECTOR FIELD

x

^{2}+ y

^{2}+z

^{2}=4, z≤0 oriented by a downward normal.

**F**=(2y-z)

**i**+(x+y

^{2}-z)

**j**+(4y-3x)

**k**

## Homework Equations

∫∫

_{S}Δ χ

**F**d

**S**=∫

_{∂S}

**F**.d

**s**

the triangle is supposed to be upside down.

## The Attempt at a Solution

myΔχF = 3i +2j-1k

my N i got 2Xi + 2Yj and since Z≤0

I'm not so sure what to next

∫∫(6X+4Y)dxdy

in the example in the book it said something on a similar exercise that by the symter og D and that fact that 6x and 4y are odd functions are odd functions we have the double integral = 0

is it correct and permanant to go with that fact because I also got 0 on the right hand side. ?