# Thread: [SOLVED] Need help with application of intergral problem

1. ## [SOLVED] Need help with application of intergral problem

sloved

2. Originally Posted by peter0516
A 20-lb. monkey is attached to a 50-ft. chain that weighs 0.5 lb. per (linear) foot. The other end of the chain is attached to the 40-ft.-high ceiling of the monkey's cage. Find the amount of work the monkey does in climbing up her chain to the ceiling.

I have no clue were to start and its making me mad

So we need to figure out the force equation since

$\displaystyle W=\int F dx$ (Force times distance)

Since pounds are a force let find the equation

When the monkey starts on the ground the only weight it carries is itself (P for pounds)

$\displaystyle P(0)=20$

When the monkey is at the top he will be holding 25 ft of chain and each foot weight 1/2 pound so we get

$\displaystyle P(40)=20+25\left( \frac{1}{2}\right)=\frac{65}{2}$

So the slope of this line is

$\displaystyle m=\frac{\frac{65}{2}-20}{40-0}=\frac{\frac{65-40}{2}}{40}=\frac{25}{80}=\frac{5}{16}$

$\displaystyle P(x)=\frac{5}{16}x+20$

So the work in the integral of Force (pounds ) over distance

$\displaystyle \int_{0}^{40}\left( \frac{5}{16}x+20 \right)dx$

3. ## k

ok so then i would do the anti derivite of that and then plug in the numbers?