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Verifying Stokes' Theorem for this Plane

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(edited 4 years ago)
Reply 1
Avatar for marinaelise
marinaelise
OP
9
Hi everyone!
Really unsure where I am going wrong with this! any input greatly appreciated!


@RDKGames
(edited 4 years ago)
Original post by marinaelise
Hi everyone!
Really unsure where I am going wrong with this! any input greatly appreciated!
@RDKGames


Your working out is very hard to read without zooming in, at which point it's finding the right balance between bluriness and size of the text.

Anyway, you made a small rookie error in the first integral.

Regarding ∬S(∇×F)⋅dS\displaystyle \iint_S (\nabla \times \mathbf{F}) \cdot d\mathbf{S}. Your approach is very good, but you made a slip-up when you go from;

∫016(1−x)dx\displaystyle \int_0^1 6(1-x) dx

to

∫01(6−x)dx\displaystyle \int_0^1 (6-x) dx.

Once you correct this, you end up with an answer of 3. Which is in agreement with your second integral ∮CF(r)⋅dr\displaystyle \oint_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r}.
(edited 4 years ago)
Reply 3
Avatar for marinaelise
marinaelise
OP
9
Original post by RDKGames
Your working out is very hard to read without zooming in, at which point it's finding the right balance between bluriness and size of the text.

Anyway, you made a small rookie error in the first integral.

Regarding ∬S(∇×F)⋅dS\displaystyle \iint_S (\nabla \times \mathbf{F}) \cdot d\mathbf{S}. Your approach is very good, but you made a slip-up when you go from;

∫016(1−x)dx\displaystyle \int_0^1 6(1-x) dx

to

∫01(6−x)dx\displaystyle \int_0^1 (6-x) dx.

Once you correct this, you end up with an answer of 3. Which is in agreement with your second integral ∮CF(r)⋅dr\displaystyle \oint_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r}.


Ok I’m actually in awe of my stupidity ._____.

So sorry forcing you to pick this out- I thought I had done something fundamentally wrong and knew you’d have the answer!

cant thank you enough

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