Calculating Work to Empty a Water-Filled Trough

[chimbooze]

A trough is 2 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 density of water is 62 pounds per cubic foot.

Work = weight x distance traveled.

Weight = volume x density
Weight =

distance traveled = 1 - y

I'm just having issue with coming up with the volume for the cross section of the trough. If I know that, I can take the integral from 0 to 1 with respect to y.

 

[Dick]

The volume is the area of the cross section*dy. The area is a rectangle. The length is 2 and the width is the distance from -x to x, where x^6=y. Sound right? What's the area?