random spesh questions

[magneto]

hello,

how would i find the lateral surface area of the solid generated when the curve is rotated around the x axis:
y= 1/x domain [1,2]

thanks in advance

p.s i know this is not apart of the study design, but my teacher has decided to set this as one of our application SACs

[HarleyZhong]

V equals pi int a to b ((fx))^2dx
V equals pi int 1 to 2 (x^-1)^2dx
V equals pi int 1 to 2 (x^-2)dx
V equals pi(-x^-1) 1 to 2.
V equals pi((-2^-1)-(-1^-1))
V equals pi(-0.5 1)
V equals 0.5pi units cubed
Int is the integral sign, 1 to 2 in the interval. Hope this helps.

[brightsky]

let f(x) = 1/x. then the lateral surface area is given by int 2 pi f(x) sqrt(1 + [f'(x)]^2) dx from x = 1 to x = 2. it might be in your interests to google the derivation of this formula, which bears some resemblance to that of the formula used to compute the volume of a solid of revolution. the general idea is to break the solid up into a lot of frustrums and compute the lateral surface area of each frustrum.