I figured out the first half, but part B is giving me trouble A heavy rope, 60 f

Question

I figured out the first half, but part B is giving me trouble

A heavy rope, 60 ft long, weighs 0.3 lb/ft and hangs over the edge of a building 130 ft high. (Let x be the distance in feet below the top of the building. Enter x_i* as How mu ch work W is done in pulling the rope to the top of the building? Show how to approximate the required work by a Riemann sum. Express the work as an integral. Evaluate the integral. How mu ch work W is done in pulling half the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim sigma Express the work as an integral. integral^30 Evaluate the integral.

Explanation / Answer

b) Let weight of the rope when pulling up the i the section is 0.3(60-xi*) lb

work required to pull up i th interval is 0.3(60-xi*) delta x ft-lb

This requires almost the same Riemann sum except the upper limit on the sum changes.

The required work by Riemann sum is by pulling half the rope to the top of the building

W=lim n--> infinity summation of (i=1 to n/2) ((0.3(60- xi))) delta x

W=integration of (x=0 to 30)(0.3(60-x))dx

=[0.3*60(x)-0.3*(x^2)/2] from x=0 to 30

=[0.3*60(30)-0.3*(1/2)*(30)^2]-[0.3*60*(0)-0.3*(1/2)*(0)^2]

=[540-135]

=405 ft-lb

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