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How to work out a Riemann sum on a TI-83 Plus

By E-Code · updated

Press 2nd LIST (above STAT), ▶▶ to MATH and 5 for sum(, then 2nd LIST, ▶ to OPS and 5 for seq(. Type height × width, X, the first and last left edges and the width, close both brackets and press ENTER: sum(seq(X²*.5,X,0,1.5,.5)) gives 1.75.

Step by step

  1. Open LIST. 2nd STAT Press 2nd, then STAT. LIST (above STAT) has NAMES OPS MATH.
  2. Go to MATH. ▶ ▶ Press ▶ twice to the MATH tab.
  3. Pick sum(. 5 Press 5 for sum(: it adds up a list.
  4. LIST again. 2nd STAT Press 2nd, then STAT.
  5. Go to OPS. ▶ Press ▶ once to the OPS tab.
  6. Pick seq(. 5 Press 5 for seq(: it makes the list, one rectangle each.
  7. One rectangle's area. X,T,θ,n X² × . 5 , Type X² × .5 and a comma: height X² times width 0.5.
  8. Where the rectangles go. X,T,θ,n , 0 , 1 . 5 , . 5 ) ) Type X , 0 , 1.5 , .5 ) ): X runs from 0 to 1.5 in steps of 0.5, the left edges of 4 rectangles from 0 to 2.
  9. Add them up. ENTER Press ENTER.
  10. Read the sum. 1.75: the left Riemann sum of X² from 0 to 2 with 4 rectangles. The exact area is 2.667; smaller steps get closer.

What the screen shows

1.75: the left Riemann sum of X² from 0 to 2 with 4 rectangles. The exact area is 2.667; smaller steps get closer.

Look for 1.75 on the screen.

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