Answer: Using Stokess Theorem In Exercises 918, use Stokess Theorem to evaluate In each
Chapter 15, Problem 18(choose chapter or problem)
In Exercises 9 - 18, use Stokes's Theorem to evaluate \(\int_{C} \mathbf{F} \cdot d \mathbf{r}\). In each case, C is oriented counterclockwise as viewed from above.
\(\mathbf{F}(x, y, z)=x y z \mathbf{i}+y \mathbf{j}+z \mathbf{k}, \quad x^{2}+y^{2} \leq a^{2}\)
S: the first-octant portion of \(z=x^{2}\) over \(x^{2}+y^{2}=a^{2}\)
Text Transcription:
int_C F cdot dr
F(x, y, z) = xyzi + yj + zk, x^2 + y^2 leq a^2
z = x^2
x^2 + y^2 = a^2
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