Luigi0210
  • Luigi0210
Stoke's Theorem:
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Luigi0210
  • Luigi0210
Use Stoke's theorem to solve \(\large \int_{C} F~ dr \) where F(x,y,z) = and C is the boundary of part of plane 3x+y+z=3 in the first octant.
Astrophysics
  • Astrophysics
I had trouble understanding Stoke's and I've always wanted to go over it again and learn it a better way...mhm lets see if we can figure this out \[\int\limits_{C} \vec F \cdot d \vec r = \int\limits \int\limits_S curl \vec F \cdot d \vec S\] right
Luigi0210
  • Luigi0210
Not sure, I'm a bit confused because of these: http://prntscr.com/7t4ipd

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Luigi0210
  • Luigi0210
Same thing?
dan815
  • dan815
yes all same thing
Astrophysics
  • Astrophysics
Yes, you should understand the notation and what it means then I think it would be more clear hmm. I'm thinking we can pick any surface S with the boundary C.
Astrophysics
  • Astrophysics
This would be a nice question to observe haha, I sort of have an idea, but I think @dan815 @ganeshie8 @Empty would be better in teaching this, plus I can learn from them to xD.
dan815
  • dan815
|dw:1436995421444:dw|
Astrophysics
  • Astrophysics
Projection?!
dan815
  • dan815
we gotta see those intersections with xz yz and xy plane
dan815
  • dan815
we can see the 3 intersections with the 3 axis by setting x,y=0 y,z=0 x,z=0
dan815
  • dan815
|dw:1436996249413:dw|
dan815
  • dan815
thre u go not integrate over that surface area
dan815
  • dan815
|dw:1436996425783:dw|
dan815
  • dan815
F is a function of x,y so we want to refine our new surface area in terms of x and y too
dan815
  • dan815
ds=|F_x X Fy| dxdy
dan815
  • dan815
i dont remember that exactly, u can work it out though
dan815
  • dan815
|dw:1436996594088:dw|
dan815
  • dan815
there fore ds= |fx X fy| dxdy
dan815
  • dan815
your domain will be that triangle
dan815
  • dan815
|dw:1436996772371:dw|
dan815
  • dan815
|dw:1436996788233:dw|
dan815
  • dan815
|dw:1436996930190:dw|
dan815
  • dan815
finally note how Gx and Gy vectors are formed
dan815
  • dan815
|dw:1436997056399:dw|
dan815
  • dan815
|dw:1436997128852:dw|
dan815
  • dan815
and finally u can look up a proof for why the determinant of the 2 vectors gives you the area composed by them
dan815
  • dan815
but for starters u can take the formula at face cvalue how u dot v = |U||V| cos theta and U X V = |U||V| sin theta <--- area
dan815
  • dan815
as |V| sin theta is the height
dan815
  • dan815
so that would the formula for the area of a parallelogram

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