# Applications of Integrals

1. Nov 2, 2004

### Caldus

I am trying to solve a problem dealing with applying integrals to physics. Here's one that I am having trouble with:

A trough is 4 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of x^6 from x = -1 to x =1. The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot.

Here's my attempt at it:

I drew an x axis which starts at the top (and at the center) of the trough.

Volume of a small slice (horizontal slice):
Length * Width
4 * 2(-x+1)^(-1/2)dx

Weight (Force) of a small slice (horizontal slice):
Volume * Density
(4 * 2(-x+1)^(-1/2)dx)*62

Work required for small slice:
Force * Distance
((4 * 2(-x+1)^(-1/2)dx)*62)x

And then I took the integral of that between 0 and 1 and it did not work. Any ideas?

2. Nov 3, 2004

### Tide

Where did the square roots come from?