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Stewart_Calc_7ET ch16sec08
MULTIPLE CHOICE
1. Use Stokes’ Theorem to evaluate .
;
S is the part of the paraboloid lying below the plane and oriented with
normal pointing downward.
a.
0
b.
c.
d.
2. Use Stokes’ Theorem to evaluate .
;
C is the curve obtained by intersecting the cylinder with the hyperbolic
paraboloid , oriented in a counterclockwise direction when viewed from above
a.
b.
0
c.
d.
3. Use Stoke’s theorem to evaluate where and C is the
boundary of the part of the plane in the first octant.
a.
69
b.
16
c.
49
d.
0
e.
23
−3
3
−4
1
4. Use Stokes' Theorem to evaluate
S consists of the four sides of the pyramid with vertices (0, 0, 0), (3, 0, 0), (0, 0, 3), (3, 0,3)
and (0, 3, 0) that lie to the right of the xz-plane, oriented in the direction of the positive y-
axis.
a.
0
b.
12
c.
16
d.
49
e.
1
NUMERIC RESPONSE
1. Use Stoke’s theorem to calculate the surface integral where
and S is the part of the cone
2. Use Stoke’s theorem to evaluate
C is the boundary of the part of the paraboloid in the first octant. C is
oriented counterclockwise as viewed from above.
3. Use Stokes' Theorem to evaluate S consists of the top and the four sides (but
not the bottom) of the cube with vertices oriented outward.
4. Use Stoke’s theorem to evaluate
C is the curve of intersection of the plane z = x + 9 and the cylinder
5. Use Stoke’s theorem to evaluate
C is the curve of intersection of the hyperbolic paraboloid and the cylinder
oriented counterclockwise as viewed from above.
6. Find parametric equations for C, if C is the curve of intersection of the hyperbolic
paraboloid
and the cylinder oriented counterclockwise as viewed from above.
SHORT ANSWER
1. Use Stokes’ Theorem to evaluate .
;
S is the part of the ellipsoid lying above the xy-plane and oriented
with normal pointing upward.
2. Use Stokes’ Theorem to evaluate .
;
C is the boundary of the triangle with vertices , , and oriented in a
counterclockwise direction when viewed from above
