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A leaky $10-\mathrm{kg}$ bucket is lifted from the ground to a height of $14$ m at a constant speed with a rope that weighs $0.6 \mathrm{~kg} / \mathrm{m}$. 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 $14-\mathrm{m}$ level. How much work is done? (Use $9.8 \mathrm{~m} / \mathrm{s}^{2}$ for g .)$\newline$Show how to approximate the required work (in J) by a Riemann sum. (Let $x$ be the height in meters above the ground. Enter $x_{i}^{* *}$ as $x_{i}$ )$\newline$$\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(\boxed{98+35.28 x_{i}}\right) \Delta x$$\newline$Express the work (in J) as an integral in terms of $x$ (in m).$\newline$$\int_{0}^{14}(98+35.28 x$$\newline$Evaluate the integral (in J). (Round your answer to the nearest integer.)