MATH 1351 TI-85 EXERCISE XII

The TI-85 and Riemann Sums

Name: SID:

Let's estimate the areas under the graphs of some positive functions, above the x-axis, and between some x-values, say a and b. We'll do it by drawing rectangles called right boxes, whose right edge, hence height, is determined by the graph, and bases are the same lengths, delta-x.

1. Use two such boxes (computing by hand) to approximate the area under the graph of y = 1/x , from x = 1 to x = 3.	In fraction form the approximate is

2. Repeat the exercise using 3 boxes.	In fraction form the approximate is

3. Repeat the exercise using 4 boxes.	In fraction form the approximate is

Find the TI-85 command	seq	by choosing 2nd MATH from the keyboard, then MISC from the screen menu. Enter the following command sequence onto the screen

seq( (2/2)(1/(1+I(2/2)) , I , 1 , 2 , 1 )

Press ENTER and then convert the answer to fraction form. You should see the terms summed in problem 1. From the same place your found seq find sum. Choosing sum 2nd ANS should sum the sequence found above and yield the same result as in number 1. Does it?

Now use the TI to repeat numbers 2 and 3 above. The general syntax is

seq( delta-x f( a + I delta-x ) , I , 1, N, 1) followed by sum

where N is the number of boxes and delta-x = ( b - a ) / N.

4. Estimate the above area using 10 boxes.	In fraction form the approximate is

5. Estimate the above area using 100 boxes.	In fraction form the approximate is

Use 100 boxes to estimate each of the following areas:

6. The area under one positive loop of the graph of the sine curve. The approximation is

7. The area under y = x^5 from x=0 to x=2.	The approximation is

8. The area of the finite region determined by the x-axis and the graph of y = x^4 -2x^2 +1.

The approximation is

9. The area under y = e^(x^2) from x = -1 to x = 1.	The approximation is	What would be the syntax if we were using left boxes instead of right boxes to approximate the area?