Test Stokes' Theorem for the function(adsbygoogle = window.adsbygoogle || []).push({});

[itex] \vec{v} = (xy) \hat{x} + (2yz) \hat{y} + (3yz) \hat{z} /[/itex]

for the triangular shaded region

[tex] \int_{S} (\grad \times v) \dot da = \oint_{P} v \bullet dl [/tex]

for the left hand side

[tex] \int_{0}^{2} \int_{0}^{2} (-2y \hat{x} - 3z \hat{y} - x \hat{z}) \hat{x} dy dz = \int_{0}^{2} \int_{0}^{2} (-2y) dy dz = \left[ \frac{-y^2} \right]_{0}^{2} \int_{0}^{2} dz = (-4)(2) = -8 [/tex]

so far so good??

ok for hte right hand side

i) x=0, z=0, [itex] v \bullet dl = 2y dy[/itex] integration limits 0 to 2

ii) x=0, y=2, [itex] v \bullet dl = 0 dz [/itex] integration from 0 to 2

i am not sute about the last one though....

am i right with i and ii though??

thank you for any advice!

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# Homework Help: Test Stokes' Theorem for the function

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