## MathSofiya Group Title 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? 2 years ago 2 years ago

1. Libniz Group Title

what the devil is this?

2. MathSofiya Group Title

Area of a Surface of Revolution

3. Libniz Group Title

surface area ?

4. MathSofiya Group Title

yes

5. Libniz Group Title

let me make some drawing

6. MathSofiya Group Title

@TuringTest

7. Libniz Group Title

|dw:1341858624540:dw|

8. Libniz Group Title

we are taking circumference of each plate , they have height(radius) of 'y' 2 Pi r= 2 Pi y

9. MathSofiya Group Title

what if we're rotating about the y axis...would it still be 2 pi y

10. Libniz Group Title

no

11. Libniz Group Title

it would be much more complicated

12. MathSofiya Group Title

2 pi x

13. Libniz Group Title

not that simple

14. Libniz Group Title

first ,you gotta define function in term of x

15. MathSofiya Group Title

ok

16. MathSofiya Group Title

as in x= .....y....

17. MathSofiya Group Title

or x=g(y)

18. Libniz Group Title

it is too complicated unlike finding volume , we just use x axis

19. MathSofiya Group Title

ok

20. MathSofiya Group Title

|dw:1341859119434:dw|

21. MathSofiya Group Title

$S=\int 2\pi x ds$

22. MathSofiya Group Title

but the book still has (dy/dx)^2

23. MathSofiya Group Title

24. Libniz Group Title

it is 3 dimensional

25. helder_edwin Group Title

give a second to check my books it's been a long time

26. MathSofiya Group Title

ok

27. MathSofiya Group Title

Everyone abandoned me :'(

28. helder_edwin Group Title

no

29. TuringTest Group Title

30. TuringTest Group Title

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 Group Title

ok

32. TuringTest Group Title

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 Group Title

Yes

34. TuringTest Group Title

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 Group Title

36. TuringTest Group Title

yo si

37. MathSofiya Group Title

sorry I can't

38. SmoothMath Group Title

lol. That guy.

39. TuringTest Group Title

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

40. MathSofiya Group Title

I will , thanks @TuringTest .

41. TuringTest Group Title

welcome :)

42. SmoothMath Group Title

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 Group Title

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 Group Title

oh ok....thanks everyone Thanks @SmoothMath !!!

45. SmoothMath Group Title

My pleasure =D

46. TuringTest Group Title

@helder_edwin me lo mandas por favor? quiero aprender mas la terminologia en espanol

47. helder_edwin Group Title

claro!

48. helder_edwin Group Title

@TuringTest recibiste el pdf?

49. TuringTest Group Title

no, donde lo pusiste? podrias mandarme un ("link"?) o url ? ya puesto que estoy tu "fan" es posible mandar mensajes privadas