Stoke's Theorem to find ∫C F · dr?
Use stoke's theorem to find ∫C F · dr where F= -(z^3)i+ (x)j+(y^3)k and C is the curve of intersection of the plane x+2y+z=2 with the three coordinate planes i.e the lines joining (2,0,0) to (0,1,0) to (0,0,2). Thank you for your time
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Curl F= (3y^2, -3z^2, 1)
INT_C F.dr = INT_S curl F.<n>dS = INT_A curl F.( N/ IN.kI )dA , dA over XY plane
N= (1,2,1)
N.k=1
= INT_A (3y^2-6z^2+ 1) dA
z^2 = ( 2-(x+2y))^2
=INT INT (3y^2-6( 2-(x+2y))^2+ 1) dydx
The line , boundary on XY plane is x/2+y/1=1 (passing by (2,0,0) and (0.1.0)
so , limits
0<y<1-(x/2)
0<x<2