anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
You're trying to compute the area of a circle?
anonymous
  • anonymous
so say you have f(x)>0 in the first quadrant
anonymous
  • anonymous
im doing the formula for surface area , made by revolving a curve about an axis .

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
generated i should say
anonymous
  • anonymous
Ok
anonymous
  • anonymous
I don't understand that second integral you wrote.
anonymous
  • anonymous
Oh wait, yes I do.
anonymous
  • anonymous
integral 2pi * f(x) sqrt ( 1 + f ' (x) ^2 ) dx
anonymous
  • anonymous
yeah
anonymous
  • anonymous
Polpak, when you get finished can you assist me?
anonymous
  • anonymous
so my question is , why cant we just use the easier formula integral 2pi f(x) dx
anonymous
  • anonymous
what r u guys parternes?
anonymous
  • anonymous
Are you rotating around the x axis?
anonymous
  • anonymous
yes in this case
anonymous
  • anonymous
say y = x^2 from 0 to 2 , but trying to find surfacea area
anonymous
  • anonymous
But you still need to account for the way f(x) is changing over your dx
anonymous
  • anonymous
You would be fine if it were flat washers
anonymous
  • anonymous
But along the top edge there can be a lot of slopes that will change the area of the final surface.
anonymous
  • anonymous
thats true but
anonymous
  • anonymous
when you go to zero, dont they approach 2pi * r , the height
anonymous
  • anonymous
Yes, but they still have an angle.
anonymous
  • anonymous
You're ok computing the volume that way
anonymous
  • anonymous
but not the surface area.
anonymous
  • anonymous
actually its not volume
anonymous
  • anonymous
it would be the surface of a cylinder type figure, i guess, not sure
anonymous
  • anonymous
for example here, we have using my way integral 2pi x^2 dx from 0 to 2
anonymous
  • anonymous
See 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
  • anonymous
the books way is integral 2pi x^2 sqrt ( 1 + (2x)^2) dx
anonymous
  • anonymous
come back
anonymous
  • anonymous
but 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
  • anonymous
err I said that wrong
anonymous
  • anonymous
But you see what I mean.
anonymous
  • anonymous
We 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
  • anonymous
But for the line integral it doesn't come close
anonymous
  • anonymous
yeah, why is that
anonymous
  • anonymous
Let me see if I can explain.
anonymous
  • anonymous
http://www.dabbleboard.com/draw?b=Guest666913&i=0&c=d86fb2255acc9e8490af7e397d12fe9fc183a40a
anonymous
  • anonymous
You there?
anonymous
  • anonymous
http://www.twiddla.com/529576

Looking for something else?

Not the answer you are looking for? Search for more explanations.