A cable that weighs 8 Ib/ft is used to lift 750 Ib of coal up a mine shaft 600 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 x,* as x;.) lim Ax Express the work as an integral. 7 x3 - 8 * )dx Evaluate the integral. 2273/4 X ft-lb

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.