The image below is the shape of a tank that is full of water. Not shown in the picture is a spout atop the center of the top of the tank that rises 3 m above the tank. Write, but do not evaluate, an integral that represents the amount of work required to pump all of this water out of the tank through the spout that is atop the tank. 3 m 4 m

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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.