Work
Earth’s attraction The force of attraction on an object below Earth’s surface is directly proportional to its distance from Earth’s center. Find the work done in moving a weight of w lb located α mi below Earth’s surface up to the surface itself. Assume Earth’s radius is a constant r mi. 

Volumes

Find the volume of the solid generated by revolving the “triangular” region bounded by the curve y = 4/x³ and the lines x = 1 and y = 1/2 about

a. the x-axis

Work

Pumping a conical tank A right-circular conical tank, point down, with top radius 5 ft and height 10 ft, is filled with a liquid whose weight-density is 60lb/ft³. How much work does it take to pump the liquid to a point 2 ft above the tank? If the pump is driven by a motor rated at 275ft-lb/sec (1/2 hp), how long will it take to empty the tank? 

Find the lengths of the curves in Exercises 19–22.

y = x¹/² ― (1/3) x³/² , 1 ≤ x ≤ 4

Volumes

Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y = 3x⁴ , and the lines x = 1 and x = ―1 about

a. the x-axis

Work

Lifting equipment A rock climber is about to haul up 100 N (about 22.5 lb) of equipment that has been hanging beneath her on 40 m of rope that weighs 0.8 N/m. How much work will it take? (Hint: Solve for the rope and equipment separately, then add.)

Volumes

Find the volume of the solid generated by revolving the region bounded by the parabola y² = 4x and the line y = x about

d. the line y = 4