5. (a) If f(x) = x · 2*, give an estimate of the net area of the region bounded by fand the x-axis %3D on [1, 5] using the: i. L, Riemann sum ii. L, Riemann sum iii. R. Riemann sum 4 iv. M. Riemann sum (b) Does the R¸ Riemann sum give an overestimate or an underestimate of the exact area? 4

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A:

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A: Solution :

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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.