Verify

§ ².d ²³ = SS (²x²). 1³²

с

that is show that the LHS =RHS, for

in the surface

The heat

Z ph

I deform,

Stokes Theoran

Ĵ

270

S: x² + y² +2²=3 =>0

trick that I use

골

10~

S31

7²x

TX

7²x

Imagine a bubble on a CIRCULAR rim C₁,

Here &c, closed curve = §₁²₂² = § ²3₂ = § ₁₂₁

For a vector fuld we will find

different surface SS (0x²) ds₁ = ²d² | C₁=C₁=C3=C4/

&

215

1₁²

That for each

the bubble so that 11 =12² in (14)

only

x

Si

6₂ (0x²)

Sf₂ (0x²).ds₂ = Fid²³, SS (oxf) ds =

)

& F.d

have to calculate the area of a circle!/nSo by luoking at my diagrams you can

appreciate for each unusual Irregular smooth

/bubble surface S₁, S₂ and 53

a) ff (√x²).d³₁ = √ ².dr

SI

C₁

1) $ (0ײ).d³₂ = § ³.4² = & Fd²

S2

2

=)

ff ( x ²).d.² = & F₁d² = §£ F.d²

CI

S3

VX²

I have

F.d

d

d) $ (x²)² = & fid² = 6.²

Ju

JC4

a) = b) = c) = d)

S4

but in of F. d² the bubble has been flattened

planar surface and 1=1 here

₁

to a

So f

11

where

EASIEST

TO

SOLVE

Alix

да

C4

î

= F₁T +2₂3 +5h => (PXF) onds = (F₁, F₂, F) 12

=> SS (Gx²³²) •nds = SS F3 ds

F3

ds == ²0 and integral is easier.

X