Integration on a Graphics Calculator

Harry_the_cat

Harry_the_cat

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Mar 16, 2016
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I believe graphics calculators evaluate definite integrals using Simpson's rule.
When I try to evaluate \(\displaystyle \int_{0}^{\infty} 3xe^{-3x}dx \), putting in 100 as upper limit gives me the correct answer \(\displaystyle \frac{1}{3}\).
But if I put in 1000 as the upper limit, I get 3.19E-52. Can anyone explain what is going on behind the scenes and why the inconsistent answers?
 
The graph of the integrand has quite a bump near the origin that quickly dives back towards 0 (as x increases)...

graphg.png

I imagine that the calculator uses a fixed number of "strips" to evaluate an integral. The processor on the calculator may not be very powerful, therefore the number of strips might be quite low. The first x value the calculator takes will probably be at the lower limit, x=0 where f(x)=0. If the upper limit is set high then the second x value to be evaluated might be as high as x=10 and f(10)≈0.0000000000028 (in other words the calculator completely jumps over the bump region).
 
No. Apparently something is wrong. 1595243622359.pngBesides you may compute the integral by part and get 1/3.
 
Harry_the_cat said:
No I'm not doing anything wrong. Yes I know it can be done manually, but I was curious about the different answers given by a GC.
Click to expand...
I didn't mean you, but the calculator. You agree that the calculator answer is wrong. I tried with Wolfram integrator, but apparently he does symbolic and not numerical.
 
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