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\[\int\limits_{}^{}(x-y)ds\]

surface area?

ok

what is ds?

ds is the line integral which equals sqrt( (dx/dt)^2 + (dy/dt)^2 dt)

ok cool give me just a sec
i will scan in something

okay

is that dt outside the sqrt?

its outside

okay it just looks like its inside

don't do it htis way there has to be a shorter way

lol

haha I really appreciate the help, that is exactly where I got to in the problem

we could try integration by parts but that is messy
I have the answer
do you want it?

-(1/6)*t*(1+9*t^2)^(3/2)+(1/12)*t*sqrt(1+9*t^2)+(1/36)*arcsinh(3*t)+(4/27)*(1+9*t^2)^(3/2)

even the answer with the limits is messy

wait...

omg i got it one sec let me write it neatly

haha okay I sure hope so...my brain is fried lol

ok im posting this but i'm pretty sure i made a mistake somewhere but the problem is easy than we thought

that is certainly a lot easier than how we were doing it and a much cleaner answer

i messed up on my addition lol

haha around which part?

finding the antiderivative of u^(3/2)

okay I see..one dumb addition mistake lol