I expected Stokes theorem to make my life easier but these problems are even harder than the normal ones ive been doing.(adsbygoogle = window.adsbygoogle || []).push({});

Use Stokes' Theorem to evaluate [tex]\int\int_ScurlFdS[/tex]

where F(x, y, z) = < x^2*y^3*z, sin(xyz) ,xyz >

S: Part of cone [tex]y^2 = x^2 + z^2[/tex] that lies between the planes y = 0 and y = 3 oriented in the direction of the positive y - axis.

not sure about this one... I parameterized the curve C as r(t) = < 3cost, 3, -3sint > to get a curve with positive orientation induced by S having normal vector in pos-y direction...a circle in plane y = 3,

answer: 2187*pi/4

Use Stokes' Theorem to evaluate [tex]\int\int_ScurlFdS[/tex]

where [tex]F(x, y, z)=< e^{xy}*cos(z) ,x^2*z, xy >[/tex]

S: Hemisphere [tex]x = sqrt{1-y^2-z^2}[/tex] oriented in the direction of the positive x - axis.

curve C : r(t) = <0, cost, sint> ... a circle again in plane x=0, hmmm, wonder if I'm messing these up...?

answer: 0 (this seemed way too easy...everything was zero!)

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# Difficult Surface Integrals

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