x=2t
y=3t^2 0<= t <= 1
Evaluate the integral

- anonymous

x=2t
y=3t^2 0<= t <= 1
Evaluate the integral

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- anonymous

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

- myininaya

surface area?

- myininaya

ok

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## More answers

- myininaya

what is ds?

- anonymous

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

- myininaya

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

- anonymous

okay

- myininaya

is that dt outside the sqrt?

- anonymous

no its underneath atleast thats what it seems like in my book go here:http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI.aspx
The equation is the 2nd blue one

- myininaya

its outside

- anonymous

okay it just looks like its inside

- myininaya

i had to use integration by parts. it is long problem and maybe i'm going about the long way and there is a shorter way, but I got you started

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- myininaya

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

- myininaya

lol

- anonymous

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

- anonymous

I got to \[2\int\limits_{0}^{1}(2t-3t^2)(\sqrt{9t^2+1}\] and after that is where I am getting stuck trying to evaluate the integral

- myininaya

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

- myininaya

-(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)

- anonymous

yeah that is pretty messy it seems like it should be a lot easier than what we have you know. I got the same thing off of wolframalpha

- myininaya

even the answer with the limits is messy

- anonymous

yeah I know right and this is just a take home quiz idk. Its just that square root that is making messy like that

- myininaya

wait...

- myininaya

omg i got it one sec let me write it neatly

- anonymous

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

- myininaya

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

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- anonymous

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

- myininaya

i messed up on my addition lol

- anonymous

haha around which part?

- myininaya

finding the antiderivative of u^(3/2)

- anonymous

okay I see..one dumb addition mistake lol

- anonymous

I dont think I can thank you enough tho, This most certainly helped me out tremendously, I def needed some help on this problem. Thank you again

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