Surface Integral Homework: Is the Author's Solution Wrong?

[fonseh]

Homework Statement

Is the solution provided by the author wrong ? Stokes theorem is used to calculate the line integral of vector filed , am i right ?

Homework Equations

The Attempt at a Solution

To find the surface integral of many different planes in a solid , we need to use Gauss theorem , right ?

 

[Charles Link]

The author doesn't seem to specify what surface integral he is asking for. If he wants $\int F \cdot dA$, Gauss' law works for the surface enclosing a volume, and wouldn't apply here. If he wants you to evaluate $\int \nabla \times F \cdot \, dA$, you can use Stokes theorem and alternatively compute the line integral of $\oint F \cdot \, ds$ around the perimeter. $\\$ editing... If the author wants you to evaluate $\int F \cdot \, dA$, there are no shortcuts that I know of=neither Gauss' law or Stokes theorem will apply. You simply need to crank it out the long way... And none of us are infallible=it is my guess the author made a mistake.

 

[fonseh]

The author doesn't seem to specify what surface integral he is asking for. If he wants $\int F \cdot dA$, Gauss' law works for the surface enclosing a volume, and wouldn't apply here. If he wants you to evaluate $\int \nabla \times F \cdot \, dA$, you can use Stokes theorem and alternatively compute the line integral of $\oint F \cdot \, ds$ around the perimeter. $\\$ editing... If the author wants you to evaluate $\int F \cdot \, dA$, there are no shortcuts that I know of=neither Gauss' law or Stokes theorem will apply. You simply need to crank it out the long way... And none of us are infallible=it is my guess the author made a mistake.

Do you mean that the author maybe mean find the line integral and not find surface integral in this question ?

 

[LCKurtz]

Do you mean that the author maybe mean find the line integral and not find surface integral in this question ?

Frequently in such problems the author wants you to demonstrate Stokes' theorem by working it both ways. It's a learning thing.