Lab 1 - For this first lab in Calculus 172, our purpose was...

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For this first lab in Calculus 172, our purpose was to use the computing software Mathematica tohelp us approximate an integral using Left Riemann Sums.While many integrals can be computed byusing antiderivatives, some problems do not have elementary antiderivatives.An example of this isevaluating the integral ofe-x2.By using the program, we can generate a list of left end point sums whichwill lead us to an approximate answer.The idea is that, by increasing the amount of intervals used in thesum, our accuracy will increase.We started by determining the numerical value of the integral value ofe-x2from 0 to .Definingπthis value as S, we get an answer of 0.886219.Next, we used the program to estimate the value of S, ifwe were to use the left end point method in subintervals numbering 2, 4, 8, 16, 32, 64, and 128.Theresults are shown in table 1 below.20.0943756061767040440.4662480755261469480.1114038890489110816 0.0900612500324906632 0.0970317725360597764 0.10414697878414458128 0.108571595123949120.81778860687361240.3926663663077576480.1963355371063762160.09816867036585408320.04908458662625237640.0245423579593122551280.012271195255454614Table 1Table 2

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Term
Spring
Professor
Pietraho
Tags
Calculus, Numerical Analysis, Antiderivatives, Derivative, Integrals, Riemann Sums, left end, 16 0 098168670 36585408 32 0 049084586 62625237 64 0 024542357 959312255

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