A particle is moved along the x-axis by a force?

Question

A particle is moved along the x-axis by a force that measures 10/(1+x)^2 pounds at a point x feet from the origin. Find the work (in ft-lb) done in moving the particle from the origin to a distance of 9 feet.
Work done = ? ft-lb

Answer 1

Work = ∫ Fdx from x = 0 to x = 9
W = ∫ 10/ (1+x)² dx
set u = 1+x, du = dx, and
W = ∫ 10/ u² du from u = 1 to u = 10
W = 10/ (-3u³) = -10/3 [ 1/10³ - 1/1³] = -10/3 (.001 - 1)
= 3.33 ft-lb

Answer 2

Hi,
Integrate f(x) dx from 9 to 0.
W = S 10/(1+x)² ds (Remmeber it's from 0 to 9. I can't get that in this work processor.
..................|9
= -10/(x+1) |
.................0

= -10[ 1/(9+1) - 1/(0+1)]
Since this word processor is so inadequate for math, I'll leave the rest to you.

Hope this helps.
FE