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