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gvm

does the integral x/(5-x)^(1/2) dx that goes from 1 to 5 converge and if so what is the value and how do you find it?

  • one year ago
  • one year ago

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  1. princeofwetlot
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    \[\Large \int_1^5 \frac{x}{\sqrt{5-x}}dx?\]

    • one year ago
  2. gvm
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    yes that's what it looks like...so does it converge? and how do you show that it converges?

    • one year ago
  3. princeofwetlot
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    well you do this: \[\Large \lim_{t \rightarrow 5} \int_1^t \frac{x}{\sqrt{5-x}}dx\]

    • one year ago
  4. gvm
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    yup i have that so far :)

    • one year ago
  5. princeofwetlot
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    i am thinking trigonometric substitution for this...

    • one year ago
  6. princeofwetlot
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    |dw:1337935669505:dw|

    • one year ago
  7. princeofwetlot
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    \[\large \sqrt 5 \sin \theta = \sqrt x\] \[\large \sqrt 5 \cos \theta = \sqrt{5-x}\] \[\large 5 \sin^2 \theta = x\] \[\large 10 \sin \theta \cos \theta d\theta = dx\] \[\large \int \frac{x}{\sqrt{5-x}}dx = \int \frac{5\sin^2 \theta \times 10 \sin \theta \cos \theta d\theta}{\sqrt 5 \cos \theta}\] \[\large \frac{50}{\sqrt 5} \int \sin^3 \theta d\theta\] i believe that is solveable?

    • one year ago
  8. princeofwetlot
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    do you still need help?

    • one year ago
  9. gvm
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    i think i'm all set now...thank you :) i just have to ace this take home test because if i get a one hundred on it i'll get exempt from the final :D

    • one year ago
  10. gvm
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    thank yoouuuu! :)

    • one year ago
  11. princeofwetlot
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    no probs ^_^ keep practicing to see these things easier hehe

    • one year ago
  12. gvm
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    are you in college or high schoool?

    • one year ago
  13. princeofwetlot
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    college

    • one year ago
  14. gvm
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    neato :) where do you go?

    • one year ago
  15. princeofwetlot
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    probably a university you dont know lol

    • one year ago
  16. gvm
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    oh alright then...just curious cuz i'm starting colllege in the fall! weeee :D

    • one year ago
  17. princeofwetlot
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    congrats :D

    • one year ago
  18. gvm
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    thank you :) ughhh its sooo early where i live...i pulled an all nighter :O

    • one year ago
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