1. ## 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.

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?

2. 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.