A leaky 10-kg bucket is lifted from the ground to a height of 14 m at a constant speed with a rope that weighs 0.6 kg/m. Initially the bucket contains 42 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 14-m level. How much work is done? (Use 9.8 m/s2 for g.) Show how to approximate the required work (in ]) by a Riemann sum. (Let x be the height in meters above the ground. Enter x,* as x;.) lim n -+ 00 AX Express the work (in ]) as an integral in terms of x (in m). Evaluate the integral (in J). (Round your answer to the nearest integer.)