Fdtxjr

Important Resources for Dark Age Civilizations?

Arrow those variables!

What does "Puller Prush Person" mean?

How does one intimidate enemies without having the capacity for violence?

Does an object always see its latest internal state irrespective of thread?

Theorems that impeded progress

Maximum likelihood parameters deviate from posterior distributions

Why does Kotter return in Welcome Back Kotter?

How do I deal with an unproductive colleague in a small company?

What do the dots in this tr command do: tr .............A-Z A-ZA-Z <<< "JVPQBOV" (with 13 dots)

Is it possible to do 50 km distance without any previous training?

Paid for article while in US on F-1 visa?

Why is Minecraft giving an OpenGL error?

How can I prevent hyper evolved versions of regular creatures from wiping out their cousins?

How can bays and straits be determined in a procedurally generated map?

dbcc cleantable batch size explanation

Do infinite dimensional systems make sense?

A newer friend of my brother's gave him a load of baseball cards that are supposedly extremely valuable. Is this a scam?

LWC SFDX source push error TypeError: LWC1009: decl.moveTo is not a function

Perform and show arithmetic with LuaLaTeX

How to efficiently unroll a matrix by value with numpy?

Is it possible to run Internet Explorer on OS X El Capitan?

Alternative to sending password over mail?

Is it tax fraud for an individual to declare non-taxable revenue as taxable income? (US tax laws)

Setup equation to find surface area. Confused as to use x or y. Is this setup for surface area correct?

Find area of the surface obtained by rotating curve around x-axis?Calc II: Volume of Rotation About Y-AxisIntegral Calculus, right or wrong?How to compute the following double integral?Surface area of revolution formula for $x$ as a function of $y$ about the $x$ axisEllipse rotating around multiple axis'Integral using trig substitution checkHow do I find the surface area of this function $y = e^-x^2$ when it's rotated around the y-axis?How do I find the surface area of this function: $y = tan^-1x$Find surface area when this function is rotated around the y-axis. $y = frac13 x^frac32$

0

$begingroup$

I am trying to setup equations for finding the surface area when the equation is rotated around the x or y axis. is this right? wolfram gives me two different answers for each setup. Where am I going wrong? Wolfram gives me 9.79564 for i) and 13.721 for ii).

Say I have an equation:

$$y = tan^-1x$$ from $0 leq x leq 2$

My hint in my book is to setup the equation for x so:

$$tan y = x$$

and when $ x = 0$, $y = 0$ and when $x = 2$, $y = tan^-12$

and $fracdxdy = sec^2y$ which will be used for arc length.

i) So when rotating around the x-axis, I need a y either as y itself or as expressed in terms of x. If I express it as y, I need a dy right?

I also have to change the limits of integration here because the original limits were given for x but we're integrating with respect to y right?

$$SA = 2 pi int_0^tan^-12 y sqrt1 + (sec^2y)^2 dy$$

ii) So when rotating around the y-axis, I need a y either as x itself or as expressed in terms of y. If I express it as y, I need a dx right?

$fracdydx = frac11 + x^2$
$$SA = 2 pi int_0^2 x sqrt1 + (frac11 + x^2)^2 dy$$

integration

share|cite|improve this question

edited Mar 21 at 20:11

Kitty Capital

asked Mar 21 at 19:47

Kitty CapitalKitty Capital

1096

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please ask a clear question rather than explain what you're doing (which may or may not be appropriate for the question). WHAT surface area (for instance)?
  $endgroup$
  – David G. Stork
  Mar 21 at 19:51
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @DavidG.Stork noted, edited.
  $endgroup$
  – Kitty Capital
  Mar 21 at 20:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Your integrals are correct (except the second one should have a $dx$)
  $endgroup$
  – Shubham Johri
  Mar 21 at 20:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I wonder why my wolfram is giving me different answers....ohhh because they are supposed to be different!
  $endgroup$
  – Kitty Capital
  Mar 21 at 20:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ShubhamJohri feel free to jot an answer and note that different integral answers are correct here and I'll give you credit!
  $endgroup$
  – Kitty Capital
  Mar 21 at 21:02
  

  
  
  
  

 | 
show 1 more comment

0

$begingroup$

I am trying to setup equations for finding the surface area when the equation is rotated around the x or y axis. is this right? wolfram gives me two different answers for each setup. Where am I going wrong? Wolfram gives me 9.79564 for i) and 13.721 for ii).

Say I have an equation:

$$y = tan^-1x$$ from $0 leq x leq 2$

My hint in my book is to setup the equation for x so:

$$tan y = x$$

and when $ x = 0$, $y = 0$ and when $x = 2$, $y = tan^-12$

and $fracdxdy = sec^2y$ which will be used for arc length.

i) So when rotating around the x-axis, I need a y either as y itself or as expressed in terms of x. If I express it as y, I need a dy right?

I also have to change the limits of integration here because the original limits were given for x but we're integrating with respect to y right?

$$SA = 2 pi int_0^tan^-12 y sqrt1 + (sec^2y)^2 dy$$

ii) So when rotating around the y-axis, I need a y either as x itself or as expressed in terms of y. If I express it as y, I need a dx right?

$fracdydx = frac11 + x^2$
$$SA = 2 pi int_0^2 x sqrt1 + (frac11 + x^2)^2 dy$$

integration

share|cite|improve this question

edited Mar 21 at 20:11

Kitty Capital

asked Mar 21 at 19:47

Kitty CapitalKitty Capital

1096

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please ask a clear question rather than explain what you're doing (which may or may not be appropriate for the question). WHAT surface area (for instance)?
  $endgroup$
  – David G. Stork
  Mar 21 at 19:51
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @DavidG.Stork noted, edited.
  $endgroup$
  – Kitty Capital
  Mar 21 at 20:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Your integrals are correct (except the second one should have a $dx$)
  $endgroup$
  – Shubham Johri
  Mar 21 at 20:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I wonder why my wolfram is giving me different answers....ohhh because they are supposed to be different!
  $endgroup$
  – Kitty Capital
  Mar 21 at 20:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @ShubhamJohri feel free to jot an answer and note that different integral answers are correct here and I'll give you credit!
  $endgroup$
  – Kitty Capital
  Mar 21 at 21:02
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

I am trying to setup equations for finding the surface area when the equation is rotated around the x or y axis. is this right? wolfram gives me two different answers for each setup. Where am I going wrong? Wolfram gives me 9.79564 for i) and 13.721 for ii).

Say I have an equation:

$$y = tan^-1x$$ from $0 leq x leq 2$

My hint in my book is to setup the equation for x so:

$$tan y = x$$

and when $ x = 0$, $y = 0$ and when $x = 2$, $y = tan^-12$

and $fracdxdy = sec^2y$ which will be used for arc length.

i) So when rotating around the x-axis, I need a y either as y itself or as expressed in terms of x. If I express it as y, I need a dy right?

I also have to change the limits of integration here because the original limits were given for x but we're integrating with respect to y right?

$$SA = 2 pi int_0^tan^-12 y sqrt1 + (sec^2y)^2 dy$$

ii) So when rotating around the y-axis, I need a y either as x itself or as expressed in terms of y. If I express it as y, I need a dx right?

$fracdydx = frac11 + x^2$
$$SA = 2 pi int_0^2 x sqrt1 + (frac11 + x^2)^2 dy$$

integration

share|cite|improve this question

edited Mar 21 at 20:11

Kitty Capital

asked Mar 21 at 19:47

Kitty CapitalKitty Capital

1096

$endgroup$

share|cite|improve this question

edited Mar 21 at 20:11

Kitty Capital

asked Mar 21 at 19:47

Kitty CapitalKitty Capital

1096

share|cite|improve this question

edited Mar 21 at 20:11

Kitty Capital

asked Mar 21 at 19:47

Kitty CapitalKitty Capital

1096

asked Mar 21 at 19:47

Kitty CapitalKitty Capital

1096

asked Mar 21 at 19:47

Kitty CapitalKitty Capital

1096