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evaluating definite integrals involving abs(), sin, and exponent

I was using my Classpad fx-cg500 to evaluate the following expression which was a FRQ for AP Calc AB:

integral(0, 3.14, abs(sin(x^1.5))

This operation will take minutes to return an answer. I tried it on Casio fx-cg50 and it took only a few seconds. The fx-cg500 is supposedly the flagship of Casio's calculators. Casio has got to improve this problem or it is entirely useless on a test.

Meanwhile, does anyone know of a way to get around this slowness problem?

Thanks.

7 comments

Comments (7)

Dave Shaw

•

I see. This is likely a software limitation/bug, because I'm seeing it hang when attempting to G-SOLVE. Interestingly, if you allow it to run for a minute and then hit Clear, it will break the cycle and show the solution anyway. (See below)

I suppose at this point in time the Integration window in the Main app would be the go-to for numeric calculation. In the meantime, I'll share this with the R&D team to study.

James Chen

Replying to

Yes, that is exactly what I discovered too. I hope the R&D team will come up with a fix soon because i ran into this situation more than once where i had to hit the brake to get an answer. I have both the classpad and Nspire CX II CAS. But the classpad user interface is so much user friendly. I just hope it can perform a little faster than it is currently. Is Casio working on a next generation CAS model?

Dave Shaw

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Replying to

To my knowledge, there have been no announcements on new CAS models.

Dave Shaw

•

Hi James. This is expected behavior. The fx-CG500 uses exact/symbolic evaluation first if possible, and falls back to numeric approximation. In practice, this means the fx-CG500 might spend a long time analyzing an integral before giving up on a symbolic solution. Such an integrand like the example you provided has no simple closed-form antiderivative, so the device’s initial symbolic attempts are essentially futile. This results in the perception of poor performance, as the symbolic math behaves like a bottleneck in achieving the desired result in this case.

At these times the ClassPad needs to be asked for a non-exact/numerical result, rather than than an analytic (exact) result. To do this, select Integration via the Interactive > Calculation menu dropdown. Select the Numeric radio option.

The fx-CG50 uses a different computational system and is snappier for real-time definite integrals. Our flagship product in the United States is the fx-CG50, which is being superseded by the fx-CG100 later this year.

James Chen

Replying to

Hi Dave,

Thanks for the explanation and the tip, it worked!

But is there a way to default the definite integral calculation to always use numeric?

I often do the definite integral in the graphs using the G-Solve method, how do I instruct it to use the numeric method with G-Solve?

Thanks.

Dave Shaw

•

Replying to

Glad to hear it! G-Solve is inherently a numerical tool – it will always provide a decimal approximation for the definite integral of the graphed function over the chosen interval. You do not need to (and cannot) force G-Solve to be numeric; it already evaluates integrals numerically by default.

James Chen

Replying to

I tried the same integral by graphing and G-Solve. However, it just sat there spinning for ever. Is this a bug in the software? With the in-line forced numeric integral, it takes about 10 secs.

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evaluating definite integrals involving abs(), sin, and exponent

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