Lab 1 - For this first lab in Calculus 172 our purpose was to use the computing software Mathematica to help us approximate an integral using Left

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 to help us approximate an integral using Left Riemann Sums. While many integrals can be computed by using antiderivatives, some problems do not have elementary antiderivatives. An example of this is evaluating the integral of e -x2 . By using the program, we can generate a list of left end point sums which will lead us to an approximate answer. The idea is that, by increasing the amount of intervals used in the sum, our accuracy will increase. We started by determining the numerical value of the integral value of e -x2 from 0 to . Defining π this value as S, we get an answer of 0.886219. Next, we used the program to estimate the value of S, if we were to use the left end point method in subintervals numbering 2, 4, 8, 16, 32, 64, and 128. The results are shown in table 1 below. 2 0.09437560617670404 4 0.46624807552614694 8 0.11140388904891108 16 0.09006125003249066 32 0.09703177253605977 64 0.10414697878414458 128 0.1085715951239491 2 0.817788606 873612 4 0.392666366 30775764 8 0.196335537 1063762 16 0.098168670 36585408 32 0.049084586 62625237 64 0.024542357 959312255 128 0.012271195 255454614 Table 1 Table 2

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