## tdabboud Group Title x=2t y=3t^2 0<= t <= 1 Evaluate the integral 3 years ago 3 years ago

1. tdabboud Group Title

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

2. myininaya Group Title

surface area?

3. myininaya Group Title

ok

4. myininaya Group Title

what is ds?

5. tdabboud Group Title

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

6. myininaya Group Title

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

7. tdabboud Group Title

okay

8. myininaya Group Title

is that dt outside the sqrt?

9. tdabboud Group Title

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 Group Title

its outside

11. tdabboud Group Title

okay it just looks like its inside

12. myininaya Group Title

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 Group Title

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

14. myininaya Group Title

lol

15. tdabboud Group Title

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

16. tdabboud Group Title

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 Group Title

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

18. myininaya Group Title

-(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. tdabboud Group Title

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 Group Title

even the answer with the limits is messy

21. tdabboud Group Title

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 Group Title

wait...

23. myininaya Group Title

omg i got it one sec let me write it neatly

24. tdabboud Group Title

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

25. myininaya Group Title

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

26. tdabboud Group Title

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

27. myininaya Group Title

i messed up on my addition lol

28. tdabboud Group Title

haha around which part?

29. myininaya Group Title

finding the antiderivative of u^(3/2)

30. tdabboud Group Title

okay I see..one dumb addition mistake lol

31. tdabboud Group Title

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