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 2 years ago
How would you draw a cylinder for the shell method for the region that is enclosed by x = pi/2, x = pi/2 and y = cosx?
This is rotated about y = 1.
 2 years ago
How would you draw a cylinder for the shell method for the region that is enclosed by x = pi/2, x = pi/2 and y = cosx? This is rotated about y = 1.

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QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0@FoolForMath @myininaya @experimentX @shivam_bhalla @amistre64 @Zarkon @Hero Anyone?

akamushi
 2 years ago
Best ResponseYou've already chosen the best response.0the definite integrand of f(x)=cosx from pi/2 to pi/2 sinx from pi/2 to pi/2 = 1(1)=2

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0I do not want the answer. @akamushi

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0@FoolForMath @myininaya @experimentX @shivam_bhalla @amistre64 @Zarkon @Hero Anyone?

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0@FoolForMath @myininaya @experimentX @shivam_bhalla @amistre64 @Zarkon @Hero Anyone?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0@lgbasallote lol jk...idk shell using trig functions

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0The height would be 2cosx, and the radius would be cosx  (1)?

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0ie. h = 2y r = y  (1) ?

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1337558085638:dw

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0The height (which are the horizontal lines of the cylinder) would be given by h = 2cosx? And the radius would be given by r = cos(x)  (1)?

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0Wait, I think the height would be: h = 2x, due to symmetry

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1337558202025:dw

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0So then, radius is r = cos(x)  (1) for sure, right?

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0And I can restate that cos(x) as y So then, r = y +1, h = 2x = 2arccos(y), I believe.

PROSS
 2 years ago
Best ResponseYou've already chosen the best response.0now you are on the right track.

PROSS
 2 years ago
Best ResponseYou've already chosen the best response.0if you are familiar with winplot, you can make a nice 3d representation.

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0@shivam_bhalla! Yes you finally came.

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1337558589994:dw

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0I have one question for either of you: I drew a vertical line from the xaxis to the function cos(x). Can that generically be represented as y?

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.0@QRAwarrior , try this http://openstudy.com/updates/4fb44286e4b05565342a2a03 You will find it a lot more helpful :) The answer to your question you asked before is yes

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3x = pi/2, x = pi/2 and y = cosxdw:1337561871090:dw

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1337562804283:dw

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0Ok so it is: h = x y = cosx  (1)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3we only need half of this, then double the results height is a measure of arccos(y) radius is from from 1 to 2 by perspective \[2*2pi\int_{0}^{1}(y+1)*\cos^{1}(y)\ dy\]

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0I think I came up with this a few posts back

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3height is a function of x; y=cos(x) arccos(y) = x = height

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0 Ok consider this question: Find the length of y^2 = x^3 from (0,0) to (4,8) I know the formula for arclength, but I end up getting this: dw:1337563218324:dw

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1337563244465:dw

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0How the heck can you resolve the radical when you have: dw:1337563293983:dw As your argument?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3have you tried looking at it form both forms? \[\sqrt{1+(x')^2}\ or\ \sqrt{1+(y')^2}\]

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0No. I think I will try the other form, BUT the problem is that I am not sure whether to pick the POSITIVE root or the NEGATIVE root..

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3for the most part, i think you stick with the positive root

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0Why do you say "most part"

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3distance tends to be a measure in absolute value, so the positive root seems most apt

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0WOW! I just realized how EASY it is doing it wrt x.

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1337563549037:dw

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0Easy Usub. Thanks a lot amistre64. What level of education is your mathematics?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3i dunno what level it is, im guessing its at least on a 3rd grade level ;)

QRAwarrior
 2 years ago
Best ResponseYou've already chosen the best response.0Ok anyways, thanks for your help

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3youre welcome. Levelwise is difficult since im self taught for the most part of this stuff
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