(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use Stokes Theorem to evaluate the integral[itex]\oint_{C} F.dr[/itex] where F(x,y,z) = [itex]e^{-x} i + e^x j + e^z k [/itex] and C is the boundary of that part of the plane 2x+y+2z=2 in the first octant

2. Relevant equations

[itex]\oint_{C} F.dr = \int\int curlF . dS[/itex]

3. The attempt at a solution

So first out i calculated the curl and i got [itex]e^x [/itex] K

Also z=1-x-[itex]\frac{1}{2}[/itex]y

and[itex]\frac{\partial z}{\partial x} = -1[/itex]

and[itex]\frac{\partial z}{\partial y} = -\frac{1}{2}[/itex]

and [itex]\sqrt{(\frac{\partial z}{\partial x})^2 + (\frac{\partial z}{\partial y})^2 + 1}[/itex] = [itex]\sqrt{\frac{9}{4}}[/itex] = [itex]\frac{3}{2}[/itex]

To get my limits. when Z=0 the image of the plane on the xy plane is a triangle and so my limits will be x=0 to 1 and y=0 to 2-2x

so putting all this together i get

[itex]\int^{1}_{0}\int^{2-2x}_{0} (e^x k). (\frac{2i+j+2k}{3})(\frac{3}{2}) dydx[/itex]

[itex]\int^{1}_{0}\int^{2-2x}_{0} (e^x)dydx[/itex]

i have worked out these integrals and i get 2([itex]e^1 +2[\itex])

this doesnt look right but i dont know where i went wrong. i've gone over it twice

anyone throw some light on where im going wrong here?

Thanks for reading!

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# Homework Help: Use Stokes Theorem to evaluate the integral

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