Question

Challenge 2
Find the volume of infinite Gabriel's horn. Whether the equation converges or diverges.

Answer 1

the volume tends to be pi ....

Answer 2

its the surface are thats infinite

Answer 3

ya the surface area is infinite....but how do you set the equation to find the volume?

Answer 4

i believe its \[\Large \lim_{t\to\infty}\int_{1}^{t}\pi(\frac1x)^2~dx\]

Answer 5

a volume of rotation about the x axis, whose radius is defined by 1/x

Answer 6

the region it bouds is y=1/x, x-axis, line x=1 and x=b

Answer 7

x=b is fine too, but since its improper, the limit as b to inf

Answer 8

hmmm...do you know how to solve the rest of part

Answer 9

well

x^-2 integrates up to -1/x

-1/b - -1/1 = 1 - 1/b

as b to infinity, 1/b to zero

left with pi(1)

Answer 10

oh that seems easy, so the pi is volume right?

Answer 11

yes

Answer 12

pi units cubed ... whatever the units may be :)

Answer 13

so 3.141592^3 right

Answer 14

and does it converges or diverges

Answer 15

not pi^3 ... just pi units^3

well, since its goes to pi, id say thats a convergence

Answer 16

ya thats what i was like it is pi then why is it cubed lol...pi cu. units...haha

Answer 17

thanks

Answer 18

youre welcome

Answer 19

btw i need one more person to verify what u got

Answer 20

oh im sure you can find one, there are lots of smarter than mes roaming about :)

Answer 21

i dont think so...there r few calculus guys around...

Answer 22

haha.

Answer 23

well i havent worked on this specifically but i agree with @amistre64 work. everything that he did checks out.

Answer 24

am i suppose to laugh too? XD lol...now solve it

Answer 25

i agree too but i wanna make sure with the one who knows

Answer 26

@amistre64 solved it right though

Answer 27

it seams to be corect