Question

A carpet which is 5 meters long is completely rolled up. When x meters have been unrolled, the force required to unroll it further is F(x)=900/(x+1)^4 Newtons. How much work is done unrolling the entire carpet?

Answer 1

I think an integration from x=0 to x=5 is required.

Answer 2

Although I'm not sure how to convert from force to work in this case.

Answer 3

work = F.s

Answer 4

\[\int_0^5\frac{900}{(x+1)^4}dx\]
I would imagine the substitution method would work best here.

Answer 5

won't i get a negative answer there?

Answer 6

I believe you would, yes.