Today in my AP calc class we attempted to obtain the numerical integral for the function (1-cosx)/x^2 over the interval [-2,3] on a TI-83. My eyes being old and withered as they are read the interval as [-3,3] by mistake. Seeing an opportunity to review even functions we evaluated on [0,3] (ans:1.185) and doubled the result. Now for the glorious finish; we tried [-3,3] in order to verify the previous result and got a "division by zero error". ??????
Many other functions have been integrated by the students in class, both algebraically and on the TI-83. We have previously demonstrated that functions with point discontinuities can be integrated, so the division by zero result was surprising.
Finally, the class decided to let me know that the correct interval was [-2,3]!!! (students love to see ya sweat). We tried that and everything worked with an answer of 2.083.
Any ideas why [-3,3] really messes things up?? It seems all intervals [-a,a] cause a problem.
Thanks, Art Stahl Patchogue-Medford HS Long Island, NY