Stokes’ Theorem for evaluating line integrals Evaluate the line integral ∮ C F ⋅ d r by evaluating the surface integral in Stokes’ Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation. 13. F = 〈 x 2 – z 2 , y , 2 xz 〉; C is the boundary of the plane z = 4 – x – y in the first octant.
Stokes’ Theorem for evaluating line integrals Evaluate the line integral ∮ C F ⋅ d r by evaluating the surface integral in Stokes’ Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation. 13. F = 〈 x 2 – z 2 , y , 2 xz 〉; C is the boundary of the plane z = 4 – x – y in the first octant.
Stokes’ Theorem for evaluating line integralsEvaluate the line integral
∮
C
F
⋅
d
r
by evaluating the surface integral in Stokes’ Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation.
13. F = 〈x2 – z2, y, 2xz〉; C is the boundary of the plane z = 4 – x – y in the first octant.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.
3 In(3 + y) dx -
-dy, where C is the triangle with vertices (0,0), (6, 0), and (0, 12)
ху
3+y
ху
dy =
3 In(3 + y) dx -
3+ y
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