## anonymous 5 years ago x=2t y=3t^2 0<= t <= 1 Evaluate the integral

1. anonymous

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

2. myininaya

surface area?

3. myininaya

ok

4. myininaya

what is ds?

5. anonymous

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

6. myininaya

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

7. anonymous

okay

8. myininaya

is that dt outside the sqrt?

9. 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

10. myininaya

its outside

11. anonymous

okay it just looks like its inside

12. 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

13. myininaya

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

14. myininaya

lol

15. anonymous

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

16. 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

17. myininaya

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

18. 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)

19. 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

20. myininaya

even the answer with the limits is messy

21. 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

22. myininaya

wait...

23. myininaya

omg i got it one sec let me write it neatly

24. anonymous

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

25. myininaya

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

26. anonymous

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

27. myininaya

i messed up on my addition lol

28. anonymous

haha around which part?

29. myininaya

finding the antiderivative of u^(3/2)

30. anonymous

okay I see..one dumb addition mistake lol

31. 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