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. 6. F = 〈0, – x , y 〉; S is the upper half of the sphere x 2 + y 2 + z 2 = 4 and C is the circle x 2 + y 2 = 4 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. 6. F = 〈0, – x , y 〉; S is the upper half of the sphere x 2 + y 2 + z 2 = 4 and C is the circle x 2 + y 2 = 4 in the xy -plane.
Solution Summary: The author explains that the line integral and surface integral of Stokes’ Theorem 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.
6.F = 〈0, – x, y〉; S is the upper half of the sphere x2 + y2 + z2 = 4 and C is the circle x2 + y2 = 4 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.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY