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answer this please.
surface area integral
I'm done with those things, but the part making it difficult for me is the integration part. the sqrt(y^4 + y^2 + 1)
Yes. That's make me overthink. Can you help me?
@dape this is not a surface area integral.
can you find dx/dy ? 2ydy +4dx=2dy/y (2y-2/y)dy = -4dx dx/dy = 1/(2y) - y/2 (dx/dy)^2 = 1/(4y^2) - 1/2 + y^2/4 1 + (dx/dy)^2 = 1/(4y^2) + 0.5 + y^2/4 so we need to integrate 2pi*sqrt(0.25 + 0.5y^2 + y^4/4) pi * sqrt(1+y^2 + y^4) as you got @Yttrium
So what shall I do next? :D
@Coolsector that's gonna be one hell of an integral.
well lol what can i do
You are gonna have to use elliptic functions to solve it.
but @dape the integral that you wrote wont give the surface area
yeah i agree @Coolsector
Something seems off, I'm getting a negative answer.
maybe we need another approach
btw, how did you get that kind of high smarscore?
what is it ? lol
@dape , i know that it is tempting to write the differential dx or dy but we really need to work with ds (the length) http://tutorial.math.lamar.edu/Classes/CalcII/SurfaceArea.aspx look at surface area formulas there
the hell!! i wrote : so we need to integrate 2pi*sqrt(0.25 + 0.5y^2 + y^4/4) pi * sqrt(1+y^2 + y^4) but it should be 2pi*sqrt(0.25 + 0.5y^2 + y^4/4) pi * sqrt(1+2y^2 + y^4)
so pi sqrt((y^2+1)^2) pi(y^2+1) !!!
that is easy to integrate.. just a calculation mistake
so the surface area is pi * (y^3/3 + y) from 1 to 3 which is 28 and 2/3 times pi
|dw:1378287223929:dw| first we need to write the formula, since we have the notation about the x-axis, surface area is: on the board then we pick the 2nd definition of ds since we are given 1 <= y <= 3 as the bounds.
@ⒶArchie☁✪ i found the problem look at my last responses no point in doing it all over again.
so for our problem we can write like that on the board, then....
well I'm just explaining it to Yttrium, so he is all confirmed.
@Yttrium, would you like me to continue with this problem or you seem alright with it now?
Yeah, you're right, we have to use the differential curve length, not just dy.
I know how to solve this, but since Yttrium is not available at the moment. I'll just hold...
I found the error. And it easy, indeed. :D