In this problem we will see how to use Riemann Sums to calculate ln(2). (a) According to the Fundamental Theorem of Calculus which bound b is needed to get 1 dx In(2)? Show your work. (b) Draw the rectangular figure corresponding to a left endpoint Riemann sum with n = 5 rectangles with equal bases. Is this an over or an under estimate? 1 Y = 1 (c) Give a clear explanation of how to estimate/calculate In(2) to within an accuracy of ɛ, for example, ɛ = 0.01. Specifically how many subdivisions are needed?

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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.