(a) Use Stokes Theorem to evaluate C F dr, where F(x, y, z) x 2 y i 1 3 x 3 j xy k and C is the curve of intersection of the hyperbolic paraboloid z y 2 x 2 and the cylinder x 2 y 2 1, oriented counterclockwise as viewed from above (b) Graph both the hyperbolic paraboloid and the cylinder with doma...

a S is the part of the surface y x that lies above the unit d ...

(a) Use Stokes Theorem to evaluate C F dr, where F(x, y, z) = x...

Question:

(a) Use Stokes’ Theorem to evaluate ʃ_C F • dr, where F(x, y, z) = x²y i + 1/3 x³ j + xy k and C is the curve of intersection of the hyperbolic paraboloid z = y² - x²and the cylinder x² + y² = 1, oriented counterclockwise as viewed from above.
(b) Graph both the hyperbolic paraboloid and the cylinder with domains chosen so that you can see the curve C and the surface that you used in part (a).
(c) Find parametric equations for C and use them to
graph C.