Posted by Brian on Sunday, November 3, 2013 at 5:56pm.
A cable that weighs 1.5 lb/ft is used to lift 700 lb of coal up a mineshaft that is 400 ft deep. Find the work done.

Calculus II  Steve, Sunday, November 3, 2013 at 8:22pm
Consider the cable as a whole lot of little cable bits, each of which must be lifted a different distance. The bits at the top only have to be lifted a little way, the bits near the bottom have to be lifted a long way.
The 700 lb load has to go all the way up.
Each little piece of length dx weighs 1.5 dx and has to be lifted a distance of x feet.
The work done to lift each bit is its weight * the distance lifted. So, the whole job done is
∫[0,400] 1.5x + 700 dx
multiply the lot by a conversion factor if you want Newtons instead of ftlbs. 
Calculus II  Brian, Sunday, November 3, 2013 at 10:03pm
Wow this problem is easier than I thought it was. Thanks.