Perform the following problems: a) Consider the integral (image 1). Use the simple rule and also the trapezoid compound rule (using 6 intervals) to calculate an approximation of I. Then compare approximations. b)Consider the integral (image 2). Use the simple rule and also the Simpson's compound rule using 4 intervals (in total there would be 8 subintervals, that is: m = 4, 2m = 8) to calculate a approximation of J. Then compare the approximations
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.
a) Consider the
b)Consider the integral (image 2). Use the simple rule and also the Simpson's compound rule using 4 intervals (in total there would be 8 subintervals, that is: m = 4, 2m = 8) to calculate a approximation of J. Then compare the approximations.
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