Integral A = cosh(x) dx gives the area under the curve of cosh(x) between the interval of [0 1] and the integral M, = S xcosh(x)dx gives the first moment of this area with respect to gives the first moment of this area with respect to y-axis. If the longitudinal center of this area is caleulated by i = M,/A, caleulate longitudinal center (X) of the area. Use Simpson's method with 21 equally spaced points for the integral calculations.

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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.