Calculus 3 Line integral | Mathematics | Page 1

teal flume Apr 23, 2023, 1:02 AM

#

When I am converting this to a double integral, I am not sure what the f and g of F = <f,g> are. (number 24 btw)

cloud wadiBOT Apr 23, 2023, 1:02 AM

#

teal flume When I am converting this to a double integral, I am not sure what the f and g o...

#

Wait patiently for a helper to come along.
Once someone helps you, say thank you and close the thread with: ```diff
+close

teal flume Apr 23, 2023, 1:03 AM

#

Number 24 btw

sonic portal Apr 23, 2023, 2:33 AM

#

itll be the line integral over $C_2$ - the line integral over $C_1$ = $A = \int_{C_2}{ds} - \int_{C_1}{ds}$ so just parameterise both the curves and compute the line integral

rose cypressBOT Apr 23, 2023, 2:34 AM

#

madlad-mathemagician

sonic portal Apr 23, 2023, 2:39 AM

#

what exactly do u have trouble in

#

is it paramterising

teal flume Apr 23, 2023, 2:40 AM

#

yeah I am unsure of parameterizing it correctly

#

how exactly do I get the parameterization of the second curve?

#

I know how to do it for the first curve

wicked ember Apr 23, 2023, 2:41 AM

#

wdym second curve

#

the line?

#

straight one

teal flume Apr 23, 2023, 2:42 AM

#

yes

wicked ember Apr 23, 2023, 2:42 AM

#

that's just x=t y=√2/2

#

from -√2/2≤t≤√2/2

teal flume Apr 23, 2023, 2:43 AM

#

wait it was that simple the whole time?

#

lol

wicked ember Apr 23, 2023, 2:43 AM

#

yes

#

lmao

teal flume Apr 23, 2023, 2:43 AM

#

bruh lol

#

also

#

when I am using the area of a plane region by line integrals, there were some questions needing me to use green's theorem for flux and circulation, I was wondering what is the difference between those two and when do I know when to use em?

wicked ember Apr 23, 2023, 2:45 AM

#

circulation is vectors inline with the path, flux is vectors perpendicular to the path

#

Green's for flux converts from flux integrals which are a pain to a comparatively simpler double integral, telling the difference in usage is something you'll pick up over time and doing practice questions

teal flume Apr 23, 2023, 2:50 AM

#

odidk let me show you an example problem I

#

#

^ I tried using the circulation greene theorem and it straight up gave me zeroes for the partials

#

However when I used flux I got an actual answer, so is that what you mean by ill pick it up overtime from practice)

wicked ember Apr 23, 2023, 2:52 AM

#

yes

#

it's nuance in telling the difference between flux and circulation integrals, unless you want to memorise all the telltales on their own

teal flume Apr 23, 2023, 2:54 AM

#

So try either one and hope itll work in monkey bananna term?

wicked ember Apr 23, 2023, 2:57 AM

#

not really, circulation integral is a path integral, flux integral is a surface integral

teal flume Apr 23, 2023, 3:02 AM

#

so if I looked based off this question

#

would I know whether to use cirulation or flux green theorem

#

my understanding/knowledge may be a bit off, but based off what i knew I thought it was cirulation

#

wicked ember Apr 23, 2023, 3:32 AM

#

teal flume

you used the divergence form of greens theorem here

#

divergence=flux/volume

teal flume Apr 23, 2023, 3:35 AM

#

okay thanks for the help

#

+close

#Calculus 3 Line integral