A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
im stumped calculus circumference arc. how come we cant use integral C(x)dx to find surfacea area. C(x) is the circumference so its 2pi*r , and dx is the thickness.
so why isnt surface area integral 2pi * r * dx
instead it is integral 2pi y sqrt ( 1 + dy/dx^2)dx
anonymous
 5 years ago
im stumped calculus circumference arc. how come we cant use integral C(x)dx to find surfacea area. C(x) is the circumference so its 2pi*r , and dx is the thickness. so why isnt surface area integral 2pi * r * dx instead it is integral 2pi y sqrt ( 1 + dy/dx^2)dx

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You're trying to compute the area of a circle?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so say you have f(x)>0 in the first quadrant

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0im doing the formula for surface area , made by revolving a curve about an axis .

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0generated i should say

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't understand that second integral you wrote.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0integral 2pi * f(x) sqrt ( 1 + f ' (x) ^2 ) dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Polpak, when you get finished can you assist me?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so my question is , why cant we just use the easier formula integral 2pi f(x) dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what r u guys parternes?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you rotating around the x axis?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0say y = x^2 from 0 to 2 , but trying to find surfacea area

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But you still need to account for the way f(x) is changing over your dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You would be fine if it were flat washers

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But along the top edge there can be a lot of slopes that will change the area of the final surface.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when you go to zero, dont they approach 2pi * r , the height

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, but they still have an angle.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You're ok computing the volume that way

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but not the surface area.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0actually its not volume

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it would be the surface of a cylinder type figure, i guess, not sure

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for example here, we have using my way integral 2pi x^2 dx from 0 to 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0See you're way makes the assumption that along the top edge for a tiny dx, that the length of the line of the function = dx.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the books way is integral 2pi x^2 sqrt ( 1 + (2x)^2) dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but it doesn't. The length of the line for a small dx is proportional the the square root of the square of dy^2 + dx^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0err I said that wrong

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But you see what I mean.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We are ok with the area under the curve assuming that as we take smaller and smaller values for dx, the area approaches f(x) * dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But for the line integral it doesn't come close

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let me see if I can explain.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0http://www.dabbleboard.com/draw?b=Guest666913&i=0&c=d86fb2255acc9e8490af7e397d12fe9fc183a40a
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.