Section 1 Goals
After completing your work on this section, you should be able to:
- Interpret geometrically the surface integral of a vector field \(\vec{F}(x,y,z)\) over an oriented surface \(S\) as the flow of the vector field through the surface \(S\) in the direction of the orientation.
- Set up and evaluate the surface integral of a vector field \(\vec{F}(x,y,z)\) over an oriented surface \(S\text{.}\)
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Use predetermined formulas to set up and evaluate the surface integral of a vector field \(\vec{F}(x,y,z)\) over an oriented surface \(S\) in the special cases when:
- \(S\) is the graph of some function.
- The cross-sections of \(S\) are concentric circles.
- Recognize that the surface integral of a vector field \(\vec{F}(x,y,z)\) over an oriented surface \(S\) is dependent on the orientation of \(S\) and know how to modify the integral formula when a parameterization is orientation-reversing.