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A leaky $10\text{-kg}$ bucket is lifted from the ground to a height of $14\, \text{m}$ at a constant speed with a rope that weighs $0.6\, \text{kg/m}$. Initially the bucket contains $42\, \text{kg}$ of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the $14\, \text{m}$ level. How much work is done? (Use $9.8\, \text{m/s}^2$ for $g$.) Show how to approximate the required work (in $\text{J}$) by a Riemann sum. (Let $x$ be the height in meters above the ground. Enter $x_i^*$ as $x_i$.)