Use the Midpoint Rule to approximate

with *N* rectangles where *N = 10* and *50*.

Using Integral (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:*, typex^2+1 . - At the prompt,
*Lower x limit : -10*, type . - At the prompt,
*Upper x limit : 10*, type . - Use the arrow keys to move to
*Plot Integrand (Rectangle)*and press . - At the prompt,
*Minimum y : -10*, type . - At the prompt,
*Maximum y : 10*, type . - You will now see the graph of the function.
- Each time that you type uppercase
the value of
*n*will be increased by one and by typing lowercase you will decrease*n*by one. Proceed to make*n=10*. - Press to pick the midpoint method
and you get the following: