Homework SourseConsider F and C defined below Fxyz x2y i 13x3 j xy k C i
Consider F and C defined below.
F(x,y,z) = x^2y i + (1/3)x^3 j + xy k
C is the curve of intersection of the hyperbolic paraboloid z = y^2-x^2 and the cylinder x^2+y^2 = 16 oriented counterclockwise as viewed from above.
(a) Use Stokes\' Theorem to evaluate ?C F
F(x,y,z) = x^2y i + (1/3)x^3 j + xy k
C is the curve of intersection of the hyperbolic paraboloid z = y^2-x^2 and the cylinder x^2+y^2 = 16 oriented counterclockwise as viewed from above.
(a) Use Stokes\' Theorem to evaluate ?C F
Solution
x^2+y^2 = 16
put x=4cos(t)
y^2=16-16cos2(t)=16sin2(t)
y=4 sint(t)
z= z = y^2-x^2 =16sin2(t)-16cos2(t)=16cos(2t)
