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Multivariable calculus

Course: Multivariable calculus > Unit 5

Lesson 5: Stokes' theorem
Math
Multivariable calculus
Green's, Stokes', and the divergence theorems
Stokes' theorem
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Stokes' theorem

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Problem

Assume that S is an outwardly oriented, piecewise-smooth surface with a piecewise-smooth, simple, closed boundary curve C oriented positively with respect to the orientation of S.
\oint, start subscript, C, end subscript, left parenthesis, 4, y, \imath, with, hat, on top, plus, z, cosine, left parenthesis, x, right parenthesis, \jmath, with, hat, on top, minus, y, k, with, hat, on top, right parenthesis, dot, d, r
Use Stokes' theorem to rewrite the line integral as a surface integral.
\iint, start subscript, S, end subscript, left parenthesis
\imath, with, hat, on top, plus
\jmath, with, hat, on top, plus
k, with, hat, on top, right parenthesis, dot, d, S
Stuck?
Stuck?