x=2t
y=3t^2 0

Question

x=2t
y=3t^2        0<= t <= 1

Evaluate the integral

anonymous · Answer

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

myininaya · Answer

surface area?

myininaya · Answer

ok

myininaya · Answer

what is ds?

anonymous · Answer

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

myininaya · Answer

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

anonymous · Answer

okay

myininaya · Answer

is that dt outside the sqrt?

anonymous · Answer

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 · Answer

its outside

anonymous · Answer

okay it just looks like its inside

myininaya · Answer

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

myininaya · Answer

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

myininaya · Answer

lol

anonymous · Answer

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

anonymous · Answer

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 · Answer

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

myininaya · Answer

-(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 · Answer

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 · Answer

even the answer with the limits is messy

anonymous · Answer

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 · Answer

wait...

myininaya · Answer

omg i got it one sec let me write it neatly

anonymous · Answer

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

myininaya · Answer

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

anonymous · Answer

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

myininaya · Answer

i messed up on my addition lol

anonymous · Answer

haha around which part?

myininaya · Answer

finding the antiderivative of u^(3/2)

anonymous · Answer

okay I see..one dumb addition mistake lol

anonymous · Answer

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