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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Test Stokes' Theorem for the function

**Physics Forums | Science Articles, Homework Help, Discussion**