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Math Help - Why is TI-Interactive so bad at integrating?

  1. #1
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    Why is TI-Interactive so bad at integrating?

    Hello!

    Today i asked TI-interactive for doing this:
    integral(abs(sin(x*2*pi)),x)

    But the answer is exactly the same as I typed!?

    After all TI was able to answer this one:
    integral(sin(x*2*pi),x) = ............

    From this answer I was able to integrate the first one myself and I ended up with:
    integral(abs(sin(x*2*pi)),x) = (2*floor(2*x) - cos(pi*mod(2*x,1))) / (2*pi)

    Now I discovered that the method that TI uses when it isn't able to integrate is very inexact.

    Asking TI:
    integral(abs(sin(x*2*pi)),x,5,63) = 36.9238551611

    Making use of my integration:
    integral(abs(sin(x*2*pi)),x,5,63) = 116/pi = 36.9239467973


    Now I have two questions:
    What is the name of the method which TI uses in a situation like this?
    How comes it that TI isn't able to integrate a simple function, which I am able to integrate?
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  2. #2
    A Plied Mathematician
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    Hmm. I plugged that integral into Mathematica, and it spit out the exact answer: 116/\pi. And I have Mathematica 4, an old version. Perhaps your TI doesn't have a robust enough algorithm to handle an integral like that. This goes to my usual modus operandi: use calculators for less-intensive quick computations. I have a TI-85, and I've never needed anything beyond that for a calculator. But if you want to do any serious symbolic work, use Mathematica, and if you want to do any serious numerical work, use MATLAB. That's my opinion.
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