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anonymous

  • 4 years ago

**Calc2 Help** Surface Area generated by the curve y=x^3/2 from x = 0 to 3 about the x-axis.

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  1. amistre64
    • 4 years ago
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    so whats our integral look like?

  2. amistre64
    • 4 years ago
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    \[2pi\int \sqrt{y^2(1+dy^2)}dx\]

  3. anonymous
    • 4 years ago
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    der is 3y^2/3

  4. anonymous
    • 4 years ago
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    i mean x..

  5. amistre64
    • 4 years ago
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    3-2 = 1 3/2 x^1/2 is our derivative

  6. anonymous
    • 4 years ago
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    http://www.wolframalpha.com/input/?i=derivative+x%5E3%2F2

  7. amistre64
    • 4 years ago
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    \[2pi\int \sqrt{(x^{3/2})^2(1+(\frac{3}{2}x^{1/2})^2)}dx\] \[2pi\int_{0}^{3} \sqrt{x^3(1+\frac{9}{4}x)}dx\]

  8. anonymous
    • 4 years ago
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    you can square the 4, so now it's just pi outside the integral.

  9. amistre64
    • 4 years ago
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    is that:\[x^{3/2}\]or \[\frac{1}{2}x^3\]???

  10. anonymous
    • 4 years ago
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    where??

  11. amistre64
    • 4 years ago
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    your y= x^3/2

  12. amistre64
    • 4 years ago
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    is it:\[y=x^{3/2}\] or \[y=\frac12 x^3\]???

  13. anonymous
    • 4 years ago
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    oh it is y = (x^3)/2

  14. amistre64
    • 4 years ago
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    ahh, ok

  15. anonymous
    • 4 years ago
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  16. amistre64
    • 4 years ago
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    let me fix up my int then :) \[2pi\int \sqrt{(\frac{x^{3}}{2})^2(1+(\frac{3}{2}x^{2})^2)}dx\] \[2pi\int_{0}^2 \sqrt{(\frac{x^{6}}{4})(1+(\frac{9}{4}x^{4}))}dx\] \[2pi\int_{0}^2 \sqrt{(\frac{x^{6}}{4})(\frac{4+9x^4}{4})}dx\] \[2pi\int_{0}^2 \sqrt{(\frac{4x^6+9x^{10}}{16})}dx\] \[\frac{pi}{2}\int_{0}^2 \sqrt{4x^6+9x^{10}}dx\]

  17. amistre64
    • 4 years ago
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    doesnt really pretty up does it :)

  18. anonymous
    • 4 years ago
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    ok so how did you bring the x^3/2 inside the sqrt??

  19. anonymous
    • 4 years ago
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    haha all these things are freaking ugly!!

  20. amistre64
    • 4 years ago
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    i undid it, for example \[\sqrt{a^2b}=a\sqrt{b}\]so to put it back in; square it

  21. TuringTest
    • 4 years ago
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    why did you not finish prettying it amistre?

  22. anonymous
    • 4 years ago
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    I tried it and got an ugly big number..

  23. amistre64
    • 4 years ago
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    lol, cause this math latex is slowing my computer like mole asses

  24. TuringTest
    • 4 years ago
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    lol\[\frac{\pi}2\int_{0}^{2}x^3\sqrt{4+9x^4}dx\]now it's beautiful!

  25. anonymous
    • 4 years ago
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    \[2/3 * (4x^6 + 9x^(10))^(3/2)\]

  26. amistre64
    • 4 years ago
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    still a bit yucky :) but im sure it trigs up nice http://www.wolframalpha.com/input/?i=integrate+%28pi%2F2%29%28sqrt%284x%5E6%2B9x%5E10%29%29+from+0+to+2

  27. amistre64
    • 4 years ago
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    sqrt(tan^2) if im not mistaken

  28. anonymous
    • 4 years ago
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    @amistre.. 52.1416 didn't work. :/

  29. amistre64
    • 4 years ago
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    im not the expert at plugging into programs .... :)

  30. TuringTest
    • 4 years ago
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    what trig?\[u=4+9x^4\to du=36x^3dx\]\[xdx=\frac{du}{72}\]\[\frac{\pi}{72}\int\sqrt udu\]

  31. anonymous
    • 4 years ago
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    @Turing, that is what I had..

  32. TuringTest
    • 4 years ago
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    let me see what I get

  33. anonymous
    • 4 years ago
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    I had pi/2 integral 2/3 * (-9x^4 + 1 )^ (3/2)

  34. anonymous
    • 4 years ago
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    pi/72****

  35. anonymous
    • 4 years ago
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    with limits 144 and..

  36. anonymous
    • 4 years ago
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    1.. lol

  37. TuringTest
    • 4 years ago
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    yeah I got 52.14... as well so I would have to read back and see what you guys were doing

  38. anonymous
    • 4 years ago
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    I HATE THIS STUFF!!!!!!!

  39. amistre64
    • 4 years ago
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    does yout program say to round it to some deci spot?

  40. TuringTest
    • 4 years ago
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    hey wait, I integrated from 0 to 2, not 3 let me try again...

  41. anonymous
    • 4 years ago
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    It likes fractions..

  42. TuringTest
    • 4 years ago
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    577.041397813276 let me try to get a fraction...

  43. anonymous
    • 4 years ago
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    it says 4 or 5 sig figs..

  44. amistre64
    • 4 years ago
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    http://www.wolframalpha.com/input/?i=integrate+%282pi%29*%28x%5E3%2F2%29*%28sqrt%281%2B%283x%5E2%2F2%29%5E2%29%29+from+0+to+2 even without prettying it up and just plugging in the formula I get the same 52.

  45. amistre64
    • 4 years ago
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    52.14164475991909058699913948569216045125036230794221370364473673799360642806811915388818213592188470 see if itll do that lol

  46. TuringTest
    • 4 years ago
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    but the integral is from 0 to 3, no?

  47. anonymous
    • 4 years ago
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    52.14164475991909058699913948569216045125036230794221370364473673799360642806811915388818213592188470 HAHAHAHAHAAH.. THAT WORKED!!!

  48. amistre64
    • 4 years ago
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    0 <= x <= 2

  49. amistre64
    • 4 years ago
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    :)

  50. anonymous
    • 4 years ago
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    Sorry for the caps, my excitement overtook my fingers.

  51. TuringTest
    • 4 years ago
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    well it is obviously right, but the post says 0 to 3... I put in 0 to 2 at first as well, I must have picked up on it subconsciously

  52. anonymous
    • 4 years ago
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    You guys are badass! Now it's time for me to study and to this crap on a test tomorrow morning.. Fun....

  53. amistre64
    • 4 years ago
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    good luck :)

  54. anonymous
    • 4 years ago
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    Thank ya! Take care guys.. See you next week with a new set of problems.. This time they will not be solids of revolution, but spring related force.

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