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tdabboud

  • 4 years ago

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

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  1. tdabboud
    • 4 years ago
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    \[\int\limits_{}^{}(x-y)ds\]

  2. myininaya
    • 4 years ago
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    surface area?

  3. myininaya
    • 4 years ago
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    ok

  4. myininaya
    • 4 years ago
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    what is ds?

  5. tdabboud
    • 4 years ago
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    ds is the line integral which equals sqrt( (dx/dt)^2 + (dy/dt)^2 dt)

  6. myininaya
    • 4 years ago
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    ok cool give me just a sec i will scan in something

  7. tdabboud
    • 4 years ago
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    okay

  8. myininaya
    • 4 years ago
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    is that dt outside the sqrt?

  9. tdabboud
    • 4 years ago
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    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
    • 4 years ago
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    its outside

  11. tdabboud
    • 4 years ago
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    okay it just looks like its inside

  12. myininaya
    • 4 years ago
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    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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  13. myininaya
    • 4 years ago
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    don't do it htis way there has to be a shorter way

  14. myininaya
    • 4 years ago
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    lol

  15. tdabboud
    • 4 years ago
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    haha I really appreciate the help, that is exactly where I got to in the problem

  16. tdabboud
    • 4 years ago
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    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
    • 4 years ago
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    we could try integration by parts but that is messy I have the answer do you want it?

  18. myininaya
    • 4 years ago
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    -(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
    • 4 years ago
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    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
    • 4 years ago
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    even the answer with the limits is messy

  21. tdabboud
    • 4 years ago
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    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
    • 4 years ago
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    wait...

  23. myininaya
    • 4 years ago
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    omg i got it one sec let me write it neatly

  24. tdabboud
    • 4 years ago
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    haha okay I sure hope so...my brain is fried lol

  25. myininaya
    • 4 years ago
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    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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  26. tdabboud
    • 4 years ago
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    that is certainly a lot easier than how we were doing it and a much cleaner answer

  27. myininaya
    • 4 years ago
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    i messed up on my addition lol

  28. tdabboud
    • 4 years ago
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    haha around which part?

  29. myininaya
    • 4 years ago
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    finding the antiderivative of u^(3/2)

  30. tdabboud
    • 4 years ago
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    okay I see..one dumb addition mistake lol

  31. tdabboud
    • 4 years ago
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    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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