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## Homework Statement

Use Stokes Theorem to compute

[tex]\int_{L}^{} y dx + z dy + x dx[/tex]

where L is the circle x

^{2}+ y

^{2}+ z

^{2}= a

^{2}, x + y + z = 0

## The Attempt at a Solution

I feel like this problem shouldn't be that hard but I can't get the right answer: (pi)a

^{2}/3.

I calculated the curl of F as: -(i + j + k)

and the normal vector as:

[tex]\frac{i + j + k}{\sqrt{3}}[/tex]

So:

[tex]\int_{L}^{} y dx + z dy + x dx = \int \int -(i + j + k) \cdot (\frac{i + j + k}{\sqrt{3}}) ds = -\frac{3}{\sqrt{3}} \int \int ds[/tex]

Here's where I'm stuck. I think the integral should just be the area of the circle (pi*a

^{2}) but maybe I'm thinking about it wrong. Thanks.