An aquarium 8 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use 9.8 m/s2 for g and the fact that the density of water is1000 kg/m3.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter xi* as xi.) lim n ? ? An aquarium 8 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use 9.8 m/s2 for g and the fact that the density of water is1000 kg/m3.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter xi* as xi.) lim n ? ? n i = 1 ?x Express the work as an integral. 0 dx Evaluate the integral. JAn aquarium8m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use 9.8 m/s2forgand the fact that the density of water is1000 kg/m3.)Show how to approximate the required work by a Riemann sum. (Letxbe the height in meters below the top of the tank. Enterxi* asxi.)lim n ? ? n i = 1 ?xExpress the work as an integral. 0 dxEvaluate the integral.Jn i = 1 ?x Express the work as an integral. 0 dx Evaluate the integral. JSuppose that4J of work is needed to stretch a spring from its natural length of34cm to a length of52cm.(a) How much work is needed to stretch the spring from36cm to44cm? (Round your answer to two decimal places.)J(b) How far beyond its natural length will a force of10N keep the spring stretched? (Round your answer one decimal place.)cmA cable that weighs 8 lb/ft is used to lift 800 lb of coal up a mine shaft 650 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.) lim n?? n ?x i = 1 Express the work as an integral and evaluate. 0 dx = ft-lb

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