## Related questions with answers

Question

Use Stokes’ Theorem to evaluate ∫cF · dr, where

$F(x,y,z) = x^2yi + 1/3x^3j+xyk$

and C is the curve of intersection of the hyperbolic paraboloid

$z=y^2-x^2$

and the cylinder

$x^2+y^2=1$

oriented counterclockwise as viewed from above.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 5$\textbf{Stoke's theorem}$

$\int_C \textbf{F}\cdot d\textbf{r} = \iint_S \text{curl }\textbf{F}\cdot d\textbf{S}$

Where $S$ is the Surface whose boundary is $C$

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