jegues said:
)LCKurtz said:That is exactly the way to do the problem, but you did make a mistake. Check your sign on the z component of curl F. But where did you get that integrand for I? It should be curl F dot k which isn't 12xy + 6y2. That mistake caused all the extra work (think of it as good practice
The Stokes Theorem is a mathematical theorem that relates the surface integral of a vector field over a closed surface to the line integral of the same vector field along the boundary of the surface.
The Stokes Theorem can be a troublesome problem because it requires a strong understanding of vector calculus and the ability to visualize and manipulate three-dimensional surfaces and vector fields.
It is important to first understand the problem and what is being asked. Then, use the given information to set up the appropriate integrals and apply the Stokes Theorem formula. Visualizing the problem and breaking it down into smaller parts can also be helpful.
Some common mistakes include incorrect orientation of the surface or boundary curve, not properly converting between vector and scalar fields, and errors in setting up the integrals.
Practice is key in improving understanding and problem-solving skills for the Stokes Theorem. Working through different examples and seeking help from peers or a tutor can also be beneficial. Additionally, having a strong foundation in vector calculus and three-dimensional visualization can greatly aid in solving these types of problems.
