(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex] F(x,y,z) = (x^2y^3z)i +(sin(xyz))j +(x^2yz)k [/tex]

S is the part of the 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 postive y-axis

My question deals with orientation (see below sec 3)

2. Relevant equations

[tex] \int_c F dr = \int\int_S F dS [/tex]

3. The attempt at a solution

Alright so the boundary curve C is the circle [tex] x^2 + y^2 = 9 [/tex] [tex] y=3[/tex]

My question is why does r(t) become

[tex] r(t) = 3sin(t) i+ 3j + 3cos(t)k [/tex]

instead of

[tex] r(t) = 3cos(t) i+ 3j + 3sin(t)k [/tex]

I am assuming it has something to do with the positive orientation towards postive y axis

When I did the problem I got the exact negitive of what the answer should be

i got [tex]\frac{-2187}{4}\pi[/tex] instead of [tex]\frac{2187}{4}\pi[/tex]

so I was also going to ask if I mess up the cos and sin like i did on this one should I always get the opposite sign of the correct answer or was this just random?

Also should all Strokes theorms problems be positive answers?

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# Calc 3: Strokes Therom Orientatio Question

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