NumIntegration_UVA

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Sheet1
	Example: Compute the integral from 1 to 3 of sqrt(1+(ln t)^2) numerically, accurate to 4 decimals.
	
		You could do this in Maple. But it is also easy to do in Excel or another spreadsheet. The point of this file is to remind you how.
		I used the trapezoidal rule, which is pretty accurate, and easy to implement. You could use something fancier though (eg Simpson's rule).
		If you need an actual error estimate, refer to your MATH 1310 text.
		In practice, it is just as easy to keep doubling the number of terms n until the 4th decimal stops changing.
			I saved the results of the n=50 and n=100, to compare with the n=200 answer.
		You could get fancy about programming this, but just using "fill down" and tweaking the product factors and the final sum is quick and easy.
	
	a	0
	b	1
	n	12
	delta x	0.0833333333
			trapezoidal
	x	f(x)	rule factor	product
	0	1	1	1
	0.0833333333	1.006968613	2	2.013937226
	0.1666666667	1.0281671774	2	2.0563343549
	0.25	1.0644944589	2	2.1289889178
	0.3333333333	1.1175190687	2	2.2350381375
	0.4166666667	1.1895928564	2	2.3791857128
	0.5	1.2840254167	2	2.5680508334
	0.5833333333	1.405337908	2	2.810675816
	0.6666666667	1.5596234976	2	3.1192469952
	0.75	1.755054657	2	3.5101093139
	0.8333333333	2.0025962114	2	4.0051924228
	0.9166666667	2.3170105014	2	4.6340210029
	1	2.7182818285	1	2.7182818285		1.4657942734
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	a	0
	b	3
	n	6
	delta x	0.5
			trapezoidal
	x	f(x)	rule factor	product
	0	0	1	0
	0.5	0.25	2	0.5
	1	1	2	2
	1.5	2.25	2	4.5
	2	4	2	8
	2.5	6.25	2	12.5
	3	9	1	9		9.125
Sheet3