Verifying Stokes’ Theorem Verify that the line integral and the surface integral of Stokes ’ Theorem are equal for the following vector fields, surfaces S. and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation. 7. F = 〈 x , y , z 〉 ; S is the paraboloid z = 8 – x 2 – y 2 , for 0 ≤ z ≤ 8, and C is the circle x 2 + y 2 = 8 in the xy -plane.
Verifying Stokes’ Theorem Verify that the line integral and the surface integral of Stokes ’ Theorem are equal for the following vector fields, surfaces S. and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation. 7. F = 〈 x , y , z 〉 ; S is the paraboloid z = 8 – x 2 – y 2 , for 0 ≤ z ≤ 8, and C is the circle x 2 + y 2 = 8 in the xy -plane.
Solution Summary: The author explains the Stokes' Theorem, wherein the line integral and surface integral are equal.
Verifying Stokes’ TheoremVerify that the line integral and the surface integral of Stokes’ Theorem are equal for the following vector fields, surfaces S. and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation.
7.F = 〈x, y, z〉 ; S is the paraboloid z = 8 – x2 – y2, for 0 ≤ z ≤ 8, and C is the circle x2 + y2 = 8 in the xy-plane.
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.
a=7 b=9 c=9
Let a, b and c be the last three digits of your student ID and let demaxta,b,c).
How many points are there on the surface 2 = dx +y such that the tangent plane to the surface is parallel to the plane
dx +y+2 0
Use Stokes' Theorem to evaluate Use Stokes' Theorem to evaluate ∫C F · dr where C is oriented counterclockwise as viewed from above.
F(x, y, z) = yzi + 3xzj + exyk,
C is the circle x2 + y2 = 4, z = 6.
6. Use Stokes theorem to evaluate §. F·dr, where F = (-3y² , 4z, 6x) and C
is the triangle in the plane z = ½ y with vertices (2,0, 0), (0, 2, 1) and (0, 0, 0)
with a counterclockwise orientation looking down the positive z-axis.
University Calculus: Early Transcendentals (4th Edition)
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