Let \(F = \langle xyz, xy, x^2yz \rangle\).
Use Stokes' Theorem to evaluate \(\iint_S \text{curl}\mathbf{F} \cdot d\mathbf{S}\), where
S consists of the top and the four sides (but not the bottom) of the cube with one corner at (-1,-1,-1) and
the diagonal corner at (5,5,5).
Hint: Use the fact that if \(S_1\) and \(S_2\) share the same boundary curve C that
\(\iint_{S_1} \text{curl}\mathbf{F} \cdot d\mathbf{S} = \int_C \mathbf{F} \cdot d\mathbf{r} = \iint_{S_2} \text{curl}\mathbf{F} \cdot d\mathbf{S}\)
Check Answer
Question 4
Score on last try: 0 of 1 pts. See Details for more.
You can retry this question below
Let \(\mathbf{F} = \langle 8x + y^2, 7y + z^2, 3z + x^2 \rangle\).
Use Stokes' Theorem to evaluate \(\int_C \mathbf{F} \cdot d\mathbf{r}\), where
C is the triangle with vertices (3,0,0), (0,3,0), and (0,0,3), oriented counterclockwise as viewed from
above.
