y=x^4, y=64x about the x axis.
2) The swimming pool is round, with a 8.5 foot radius. It is 9 feet tall and has 6.5 feet of water in it.
How much work is required to remove all of the water by pumping it over the side? Use the physical definition of work, and the fact that the weight of the contaminated water is 63.3lbs/ft^3
2) The swimming pool is round, with a 8.5 foot radius. It is 9 feet tall and has 6.5 feet of water in it.
How much work is required to remove all of the water by pumping it over the side? Use the physical definition of work, and the fact that the weight of the contaminated water is 63.3lbs/ft^3

The 2 curves intersect at (0,0) and (4,256)
The volume of revolution about the xaxis is ∫πy² dx from a to b. The top function is y = 64x and the bottom function is y=x^4
In this case ∫π (4096x²  x^8) dx from 0 to 4
= π [4096x^3/3  x^9/9] at 4
= 524288π/9 cubic units
The swimming pool is round, with a 8.5 foot radius. It is 9 feet tall and has 6.5 feet of water in it.
How much work is required to remove all of the water by pumping it over the side? Use the physical definition of work, and the fact that the weight of the contaminated water is 63.3lbs/ft^3
deltaW=63.3(2√((8.5)^2x^2))*9dx(x+6.5)
=1139.6∫0 to 8.5 (x+8.5)√((8.5)^2x^2))=714248 ftlb
The volume of revolution about the xaxis is ∫πy² dx from a to b. The top function is y = 64x and the bottom function is y=x^4
In this case ∫π (4096x²  x^8) dx from 0 to 4
= π [4096x^3/3  x^9/9] at 4
= 524288π/9 cubic units
The swimming pool is round, with a 8.5 foot radius. It is 9 feet tall and has 6.5 feet of water in it.
How much work is required to remove all of the water by pumping it over the side? Use the physical definition of work, and the fact that the weight of the contaminated water is 63.3lbs/ft^3
deltaW=63.3(2√((8.5)^2x^2))*9dx(x+6.5)
=1139.6∫0 to 8.5 (x+8.5)√((8.5)^2x^2))=714248 ftlb