Question

By using stokes' theorem evaluate:

Answer 1

by using stokes' theorem: \[\int\limits_{c}^{}F.dr=\int\limits_{}^{}\int\limits_{s}^{}(\Delta \times F).nds\] evaluate
\[\int\limits_{}^{}\int\limits_{s}^{}(\Delta \times F).nds\] where \[F=(x,1,-y^{2})\]

and S is the outward part of the surface \[x ^{2}+4y ^{2}+3z ^{2}=7\] that lies above the plane \[z=1\]

Answer 2

@AndrewNJ

Answer 3

@apoorvk

Answer 4

please help

Answer 5

@lgbasallote

Answer 6

I am sorry @Tushara but I haven't studied this advanced or multi-variable calculus yet, and don't have much idea of 'delta' and all. Won't be able able to help here :(

Perhaps @lalaly or @lgbasallote will know this.

Answer 7

thats ok, thanks for trying

Answer 8

lol @apoorvk

Answer 9

@A.Avinash_Goutham

Answer 10

um wat's the problem? it looks simple

Answer 11

integrate it along the curve
x2+4y2+3(1)=7
x2+4y2=4

Answer 12

i think the ans is 1

Answer 13

no the answer is zero, its ok, i figured it out :)

Answer 14

yea it's zero sorry

Answer 15

@A.avinash_Goutham - could you please explain a wee bit what we are doing here? I am just a bit curious..

Answer 16

um wat do u want to kno?

Answer 17

the same question is done as an example on dis page:
its example one, and delta F is equivalent to the curl of F

http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem.aspx