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. 14. F = 〈 x 2 – y 2 , z 2 – x 2 , y 2 – z 2 〉; C is the boundary of the square | x | ≤ 1, | y | ≤ 1 in the plane z = 0.
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. 14. F = 〈 x 2 – y 2 , z 2 – x 2 , y 2 – z 2 〉; C is the boundary of the square | x | ≤ 1, | y | ≤ 1 in the plane z = 0.
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.
14. F = 〈x2 – y2, z2 – x2, y2 – z2〉; C is the boundary of the square |x| ≤ 1, |y| ≤ 1 in the plane z = 0.
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.
Stokes' Theorem
(1.50) Given F = x²yi – yj. Find
(a) V x F
(b) Ss F- da over a rectangle bounded by the lines x = 0, x = b,
y = 0, and y = c.
(c) fc ▼ x F. dr around the rectangle of part (b).
Describe and sketch the surface given by the function.
2.Proof that any tangent plane for the surface F(
F)
point
=
0 passses through a fixed
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