Using the Riemann-sum ("Rectngl") program on a TI-83/84:

• a Riemann sum for f(x)=x² on the interval [1,3].
• An estimate for the area under the graph of f(x)=x² above the interval [1,3].
• An estimate of the total distance travelled by an object from t=1 to t=3, when its velocity at time t is f(t)=t².

1. Put your function's formula into your calculator using the [Y=] button, e.g. Y₁=X^2.
• Use Y₁ and the variable X, even if your problem calls the variable t.
  
2. Exit the [Y=] screen.
3. Press [PRGM] and (if you have multiple programs installed) scroll down to RCTNGLE. 
   Press [ENTER] to paste "prgmRECTNGL" onto your main screen.  Press [ENTER]again to start the program.
4. You will be reminded to "put the function in Y₁" if you haven't already.  If you forgot, [2nd][QUIT] and start over.
5. You will be asked for A, the left endpoint of your interval:  "A=?"  Type your value for A (1 in the example above), press enter.
6. Then you're prompted for B, the right endpoint of your interval.  Enter it (3 in the example above), and press enter.
7. Finally, you're asked for N, the number of subdivisions or subintervals or rectangles you want.  Enter that and...
8. The program will tell you the left-hand sum and right-hand sum.
9. PS:  Pressing [ALPHA][L] and [ALPHA][R] shows where the calculator has stored these sums, so typing "(L+R)/2" will give their average w/o a lot of retyping.

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