Calculus 2 work integration? Pump water out of tank?
Kobe Bryant is preparing to come out of retirement to compete for one more championship with the Los Angeles Lakers. In preparation for this Kobe pumps water out of a tank. The tank is formed by portion of the graphs below y= 2 and above y=√x between x= 0 and x= 4 rotated around they-axis. (Distances are in feet and water weighs 62.5 lb/ft³.) Calculate the work required by Kobe to pump all the water out of the tank.
- 1 month ago
W = 62.5 (integral 0 to 2) pi (y^4) (2 - y) dy
W = 62.5pi (integral 0 to 2) (y^4) (2 - y) dy
W = 62.5pi ((2/5)(y^5) - (1/6)(y^6)) | (0, 2)
W = 62.5pi ((2^6)/(5) - (2^6)/(6))
W = (62.5 * (2^6)* pi)/30
W = 418.87 ft-lbs