Evaluate the integral

four different ways:

a. analytically;

b. with a Riemann sum using m = 10;

c. with the trapezoidal rule using m = 10;

d. with Simpson’s rule using m = 10.

a.

b. Applying Riemann sums, we obtain

	f()		Product
[1]	[2]	[3]	[2] [3]
1.0
1.1	0.90909	.10	0.09091
1.2	0.83333	.10	0.08333
1.3	0.76923	.10	0.07692
1.4	0.71429	.10	0.07143
1.5	0.66667	.10	0.06667
1.6	0.62500	.10	0.06250
1.7	0.58824	.10	0.05882
1.8	0.55556	.10	0.05556
1.9	0.52632	.10	0.05263
2.0	0.50000	.10	0.05000
Total			0.66877

c. Applying the trapezoidal rule, we obtain

 

	f()	Weight		Product
[1]	[2]	[3]	[4]	[2] [3] [4]
1.0	1.00000	0.5	0.10	0.05000
1.1	0.90909	1.0	0.10	0.09091
1.2	0.83333	1.0	0.10	0.08333
1.3	0.76923	1.0	0.10	0.07692
1.4	0.71429	1.0	0.10	0.07143
1.5	0.66667	1.0	0.10	0.06667
1.6	0.62500	1.0	0.10	0.06250
1.7	0.58824	1.0	0.10	0.05882
1.8	0.55556	1.0	0.10	0.05556
1.9	0.52632	1.0	0.10	0.05263
2.0	0.50000	0.5	0.10	0.02500
Total				0.69377

d. Applying Simpson's rule, we obtain

 

	f()	Weight		Product
[1]	[2]	[3]	[4]	[2] [3] [4]
1.0	1.00000	1/3	0.10	0.03333
1.1	0.90909	4/3	0.10	0.12121
1.2	0.83333	2/3	0.10	0.05556
1.3	0.76923	4/3	0.10	0.10256
1.4	0.71429	2/3	0.10	0.04762
1.5	0.66667	4/3	0.10	0.08889
1.6	0.62500	2/3	0.10	0.04167
1.7	0.58824	4/3	0.10	0.07843
1.8	0.55556	2/3	0.10	0.03704
1.9	0.52632	4/3	0.10	0.07018
2.0	0.50000	1/3	0.10	0.01667
Total				0.69315