Riemann Sums MATLAB Assignment

1. In the command window type:

dx = .1
x = 0:dx:2
y = 3*x.2
Describe dx, x and y.

2. Next type:

format long
yl = y(1:20)
L = dx*sum(yl)
yr = y(2:21)
R = dx*sum(yr)
What are yl and yr? What are L and R? How do they compare with the true value of the integral (what is the percentage errors)?

3. Repeat the above commands, but begin with:

dx = .001
You will need to adjust the index numbers in the commands for yl and yr. What are the percentage errors of these approximations.

4. To obtain a midpoint Riemann sum type:

dx = .1
x = dx/2:dx:2-dx/2
y = 3*x.2
M = dx*sum(y)
Explain why this is a midpoint sum. For dx = .1 and dx = .001 compute the percentage errors. Make a table of percentage errors in all the above calculations.

5. Repeat all the above commands for the function
(input as y = sqrt(1 + .5*sin(x).2)) and record the answers. The value of this integral correct to 15 significant digits is: 2.27220510258726. Make a table of percentage errors as above.

6. Using complete sentences and standard mathematical notation, prepare a brief (< 1>

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