?In Exercises 5 - 8, verify Stokes's Theorem by evaluating \(\int_{C} \mathbf{F} \cdot \mathbf{T} d s=\int_{C} \mathbf{F} \cdot d \mathbf{r}\) as a lin

Chapter 15, Problem 6

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In Exercises 5 - 8, verify Stokes's Theorem by evaluating \(\int_{C} \mathbf{F} \cdot \mathbf{T} d s=\int_{C} \mathbf{F} \cdot d \mathbf{r}\) as a line integral and as a double integral.

\(\mathbf{F}(x, y, z)=(-y+z) \mathbf{i}+(x-z) \mathbf{j}+(x-y) \mathbf{k}\)

\(S: z=\sqrt{1-x^{2}-y^{2}}\)

Text Transcription:

int_C F cdot T ds = int_C F cdot dr

F(x, y, z) = (-y + z)i + (x - z)j + (x - y)k

S: z = sqrt{1 - x^2 - y^2}