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MathSofiya

just making sure I understand it.... \[S=\int_{a}^{b} 2\pi y \sqrt{1+{(\frac{dy}{dx})}^2} dx\] \[S=\int_{c}^{d} 2\pi y \sqrt{1+{(\frac{dx}{dy})}^2} dy\] \[S=\int_{a}^{b} 2\pi x \sqrt{1+{(\frac{dy}{dx})}^2} dx\] One is for revolution about the x axis...the other for revolution about the y- axis...and then we have one more equation....why?

  • one year ago
  • one year ago

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  1. Libniz
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    what the devil is this?

    • one year ago
  2. MathSofiya
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    Area of a Surface of Revolution

    • one year ago
  3. Libniz
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    surface area ?

    • one year ago
  4. MathSofiya
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    yes

    • one year ago
  5. Libniz
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    let me make some drawing

    • one year ago
  6. MathSofiya
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    @TuringTest

    • one year ago
  7. Libniz
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    |dw:1341858624540:dw|

    • one year ago
  8. Libniz
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    we are taking circumference of each plate , they have height(radius) of 'y' 2 Pi r= 2 Pi y

    • one year ago
  9. MathSofiya
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    what if we're rotating about the y axis...would it still be 2 pi y

    • one year ago
  10. Libniz
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    no

    • one year ago
  11. Libniz
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    it would be much more complicated

    • one year ago
  12. MathSofiya
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    2 pi x

    • one year ago
  13. Libniz
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    not that simple

    • one year ago
  14. Libniz
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    first ,you gotta define function in term of x

    • one year ago
  15. MathSofiya
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    ok

    • one year ago
  16. MathSofiya
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    as in x= .....y....

    • one year ago
  17. MathSofiya
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    or x=g(y)

    • one year ago
  18. Libniz
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    it is too complicated unlike finding volume , we just use x axis

    • one year ago
  19. MathSofiya
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    ok

    • one year ago
  20. MathSofiya
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    |dw:1341859119434:dw|

    • one year ago
  21. MathSofiya
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    \[S=\int 2\pi x ds\]

    • one year ago
  22. MathSofiya
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    but the book still has (dy/dx)^2

    • one year ago
  23. MathSofiya
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    @helder_edwin please help

    • one year ago
  24. Libniz
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    it is 3 dimensional

    • one year ago
  25. helder_edwin
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    give a second to check my books it's been a long time

    • one year ago
  26. MathSofiya
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    ok

    • one year ago
  27. MathSofiya
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    Everyone abandoned me :'(

    • one year ago
  28. helder_edwin
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    no

    • one year ago
  29. TuringTest
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    I didn't get your ping... weird I'll have to ask administration about that... ok, what do we ave here, let me read...

    • one year ago
  30. TuringTest
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    so you want to know why we have 4 formulas, right? my answer is that there are really only two, but each one can be seen from two different perspectives...

    • one year ago
  31. MathSofiya
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    ok

    • one year ago
  32. TuringTest
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    first consider the arc length formula:\[ds=\sqrt{1+[f'(x)]^2}dx\]now this is the formula for arc length taken from the perspective of y being a funcion of x but arc length is the same regardless of whether you look at the function as f(x) or g(y) since the arc itself will still have the same length. so we can also write\[ds=\sqrt{1+[g'(y)]^2}dy\] and as long as we are talking about the same curve they should be equal, since the arc can only have one length. make sense so far?

    • one year ago
  33. MathSofiya
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    Yes

    • one year ago
  34. TuringTest
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    now for a revolution, the formula is\[A=\int2\pi yds\]or\[A=\int2\pi xds\]depending on which axis we are going around but as I just explained above, ds (the arc length differential) can always be written two ways depending on whether we consider y a function of x or vice-versa, so each of these formulas is potentially two depending on how we look at our ds

    • one year ago
  35. helder_edwin
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    can you read spanish?

    • one year ago
  36. TuringTest
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    yo si

    • one year ago
  37. MathSofiya
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    sorry I can't

    • one year ago
  38. SmoothMath
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    lol. That guy.

    • one year ago
  39. TuringTest
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    here is a nice full explanation if you care to dig deeper http://tutorial.math.lamar.edu/Classes/CalcII/SurfaceArea.aspx

    • one year ago
  40. MathSofiya
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    I will , thanks @TuringTest .

    • one year ago
  41. TuringTest
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    welcome :)

    • one year ago
  42. SmoothMath
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    Sofiya, try to break down each integral like this: First, look at the end part, the variable you're integrating with respect to. Then, look at the limits, so you say to yourself, "Okay, travelling along x from a to b." or something like that. Then, look at the function inside and try to break that down, and what that means at each particular x. For these particular integrals, the insides have 2 basic parts. The first part has the form 2pi*something, where that something is the radius. The second part is the arclength formula. So it's calculating the arclength, and then it's multiplying that in a circle.

    • one year ago
  43. helder_edwin
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    sorry i wanted to send you something but it's in spanish. but i goes much in the same way as what @TuringTest did

    • one year ago
  44. MathSofiya
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    oh ok....thanks everyone Thanks @SmoothMath !!!

    • one year ago
  45. SmoothMath
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    My pleasure =D

    • one year ago
  46. TuringTest
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    @helder_edwin me lo mandas por favor? quiero aprender mas la terminologia en espanol

    • one year ago
  47. helder_edwin
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    claro!

    • one year ago
  48. helder_edwin
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    @TuringTest recibiste el pdf?

    • one year ago
  49. TuringTest
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    no, donde lo pusiste? podrias mandarme un ("link"?) o url ? ya puesto que estoy tu "fan" es posible mandar mensajes privadas

    • one year ago
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