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MathSofiya

  • 3 years ago

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?

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  1. Libniz
    • 3 years ago
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    what the devil is this?

  2. MathSofiya
    • 3 years ago
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    Area of a Surface of Revolution

  3. Libniz
    • 3 years ago
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    surface area ?

  4. MathSofiya
    • 3 years ago
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    yes

  5. Libniz
    • 3 years ago
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    let me make some drawing

  6. MathSofiya
    • 3 years ago
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    @TuringTest

  7. Libniz
    • 3 years ago
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    |dw:1341858624540:dw|

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

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

  10. Libniz
    • 3 years ago
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    no

  11. Libniz
    • 3 years ago
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    it would be much more complicated

  12. MathSofiya
    • 3 years ago
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    2 pi x

  13. Libniz
    • 3 years ago
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    not that simple

  14. Libniz
    • 3 years ago
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    first ,you gotta define function in term of x

  15. MathSofiya
    • 3 years ago
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    ok

  16. MathSofiya
    • 3 years ago
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    as in x= .....y....

  17. MathSofiya
    • 3 years ago
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    or x=g(y)

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

  19. MathSofiya
    • 3 years ago
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    ok

  20. MathSofiya
    • 3 years ago
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    |dw:1341859119434:dw|

  21. MathSofiya
    • 3 years ago
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    \[S=\int 2\pi x ds\]

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

  23. MathSofiya
    • 3 years ago
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    @helder_edwin please help

  24. Libniz
    • 3 years ago
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    it is 3 dimensional

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

  26. MathSofiya
    • 3 years ago
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    ok

  27. MathSofiya
    • 3 years ago
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    Everyone abandoned me :'(

  28. helder_edwin
    • 3 years ago
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    no

  29. TuringTest
    • 3 years ago
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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...

  30. TuringTest
    • 3 years ago
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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...

  31. MathSofiya
    • 3 years ago
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    ok

  32. TuringTest
    • 3 years ago
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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?

  33. MathSofiya
    • 3 years ago
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    Yes

  34. TuringTest
    • 3 years ago
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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

  35. helder_edwin
    • 3 years ago
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    can you read spanish?

  36. TuringTest
    • 3 years ago
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    yo si

  37. MathSofiya
    • 3 years ago
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    sorry I can't

  38. SmoothMath
    • 3 years ago
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    lol. That guy.

  39. TuringTest
    • 3 years ago
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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

  40. MathSofiya
    • 3 years ago
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    I will , thanks @TuringTest .

  41. TuringTest
    • 3 years ago
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    welcome :)

  42. SmoothMath
    • 3 years ago
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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.

  43. helder_edwin
    • 3 years ago
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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

  44. MathSofiya
    • 3 years ago
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    oh ok....thanks everyone Thanks @SmoothMath !!!

  45. SmoothMath
    • 3 years ago
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    My pleasure =D

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

  47. helder_edwin
    • 3 years ago
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    claro!

  48. helder_edwin
    • 3 years ago
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    @TuringTest recibiste el pdf?

  49. TuringTest
    • 3 years ago
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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

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