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## Homework Statement

Verify Stokes' theorem for the following:

[itex]F=[y^2, x^2, -x+z][/itex]

Around the triangle with vertices [itex](0,0,1),(1,0,1),(1,1,1)[/itex]

## Homework Equations

[itex]\int\int_S(curlF)\cdot ndA=\int_C F\cdot r' ds[/itex]

## The Attempt at a Solution

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For the LHS:

[itex]curlF\cdot n=2x-2y[/itex]

[itex]\int\int_S(curlF)\cdot ndA=\int_0^1 \int_0^{1-x}2x-2ydydx [/itex]

This gives zero. Also integrating over the three curves of the triangle gives zero. However, the book's answer is 1/3. Any idea what the mistake is?