H 1.	1     -1 (x3+x2) dx	Left sum; n = 4
		Right sum; n = 4
		Trapezoid sum; n = 4
		Simpson sum; n = 4
H 2.	1     0 (x3 + 2x) dx	Left sum; n = 4
		Right sum; n = 4
		Trapezoid sum; n = 4
		Simpson sum; n = 4
H 3.	3     0 (x2 + x3) dx	Left sum; n = 6
		Right sum; n = 6
		Trapezoid sum; n = 6
		Simpson sum; n = 6
H 4.	1     0 4 1 + x2 dx	Left sum; n = 6
		Right sum; n = 6
		Trapezoid sum; n = 6
		Simpson sum; n = 6

 
Use whatever technology you have at your disposal to approximate the following integrals using the stated sums.
Note: For these, answers must be accurate to at least 8 decimal places!

T 1.	1     0 4 1 + x2 dx	Left sum; n = 100
Exact Answer: = 3.141592654...		Right sum; n = 100
		Trapezoid sum; n = 100
		Simpson sum; n = 100
T 2.	1     0 e-x2 dx	Left sum; n = 100
Exact Answer: 0.7468241328...		Right sum; n = 100
		Trapezoid sum; n = 100
		Simpson sum; n = 100

E 1.	2     0 2x dx
E 2.	3     0 x3 dx
E 3.	5     1 ln x dx
E 4.	2     0 sin x dx

N 1.	2     0 x4 dx Trapezoid sum; error 0.0005
N 2.	3     0 x5 dx Trapezoid sum; 3 decimal places
N 3.	2     0 x4 dx Simpson sum; error 0.0005
E 4.	3     0 x5 dx Simpson sum; 3 decimal places

C 1. Looking at the error estimate for the trapezoid rule, by how much will the error shrink if you increase n by a factor of 10? What does this say about the increase in the number of digits of accuracy of the estimate given by the rule?

C 2. Looking at the error estimate for Simpson's rule, by how much will the error shrink if you increase n by a factor of 10? What does this say about the increase in the number of digits of accuracy of the estimate given by the rule?

C 3. Name at least two kinds of functions for which the Simpson sum always gives the exact answer, but not the trapezoid sum. Explain.

C 3. For which kind of functions does the trapezoid sum, but not the Simpson sum, give the exact answer? Explain.