Using Riemann sums, give graphical and numerical evidence for the value of the
(from the University of Arizona):
- After starting up the program, you are prompted "Would you like some
instructions?" Use the arrow keys to move to either Yes or
No and then press .
- If you choose Yes then read the instructions and press
when you are ready to proceed.
- Use the arrow keys to highlight Create Integrals and press
- Use the arrow keys to highlight Create Integral and press
- At the prompt, Enter integrand :, type
- At the prompt, Lower x limit : -10, type 0
- At the prompt, Upper x limit : 10, type 2
- Use the arrow keys to move to Plot Integrand (Rectangle) and
- At the prompt, Minimum y : -10, type 0
- At the prompt, Maximum y : 10, type 9
- You will now see the graph of the function. Press
for Arbitrary which means that
each of the points from each of the subintervals is chosen randomly.
- Press to clear the graph.
- Press uppercase
several times until n = 200.
- Again, pressing yields that the value for
the integral is 7.2806.
- Use the arrow keys to highlight Integral Operations and press
- Use the arrow keys to highlight Arbitrary Point and press
- As you keep pressing , you will
see values of the Riemann sum using powers of 2 subintervals.