Today in multivariable calculus, we were talking generally about . Before we embark on evaluating this integral, I wanted kids to guesstimate using their calculators what the value is.
The calculator image showed:
They had a conjecture as to what was going wrong when we expanded the interval… the calculator might be doing a finite number of Riemann Sums, then the width of each rectangle would be large andthe height (especially near the hump near 0) would be small.
Okay I’m describing it terribly… maybe a terrible picture will help.
Good conjecture. Great conjecture, in fact. But I doubted that the TI-83/84 uses Riemann Sums to do fnInt.
It was the end of class, so I sent my kids off with this one charge: investigate how the TI-83/84 calculates integrals, and see if you can’t explain why we’re getting funky answers for a large interval.
I figured I’d pose the question to you, if any of you are calculator saavy…
I wonder if it has to do with the fact that the calculator can only store so many (is it 15?) digits — as part of it?
PS. My very limited research has led me to the fact that the calculator does something called Gauss-Kronrod quadrature, which is a lot of gobbly gook to me right now.