This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. A heavy rope, 50 ft long, weighs 0.8 Ib/ft and hangs over the edge of a building 140 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it. Exercise (a) How much work W is done in pulling the rope to the top of the building? Click here to begin! Exercise (b) How much work W is done in pulling half the rope to the top of the building? Step 1 We will think of the work in two pieces: the work needed to lift the top half of the rope and the work needed to lift the bottom half of the rope. The work done to lift the top half of the rope follows the same thinking as in part (a). Since the top half is only 25 ft long, this portion of the work equals the following. dx ft-lb Submit Skip (you cannot come back)

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.