A bucket that weighs 4 Ib and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 44 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 Ib/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter x,* as x.) lim Ax Express the work as an integral. Evaluate the integral. ft-lb

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.