# TI-89 Titanium INTEGRATION Flaw?

• Calculators
• Switch_fx
In summary, the conversation is about a user struggling with a simple integration on their TI-89 calculator. They are looking to integrate a function involving gravitational constant, drag coefficient, mass, and velocity. The user knows the correct answer but the calculator is giving a slightly different answer. The conversation ends with suggestions for using logarithmic rules to verify that the two answers are actually the same.

#### Switch_fx

TI-89 Titanium INTEGRATION Flaw?

Ok so this is my first post, and I am in dire need of assistance. I have a big exam tomorrow and if I can't figure out why my TI-89 is screwing up this simple integration I am in some trouble...

I am looking for the integral of : 1/[G-(Cv)/M] with respect to "v"

(erroneus, G=gravitational constant, C=drag coefficient, M=mass, and V=velocity)

anyways...
I know the correct answer is : -(M/C)[ln(G-(Cv)/M)]

but my TI-89 calculator gives back the answer as:

-(M/C)[ln(|Cv-GM|)]

If anyone could please explain to me why this is so or what I am doing wrong it would be of great help...and yes I am inputting the integral in the correct fashion

Thanks to anyone who can help!

~SWITCH

If you get rid of the fraction in the denominator in the original function you will arrive at the answe your calculator does, however you should notice that these only differ by a constant and that when you integrate you always have to add on a constant of integration.

Why would I get rid of the fraction in the denominator? And if I get rid of it what do I replace it with?

You asked a question, you got an answer. Read the answer again. By the way, neither your answer nor the calculator's answer is correct!

Both are missing the added constant. d_leet's point is that your and the calculator's answer differ only by a constant.

If we leave the constant part, the calculator is right in general, as it gives the absolute value of quantity inside logarithm.

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Maybe if it's hard for you to integrate 1/(1-ax) with respect to x then you do have a problem?

Taken from 1/a onwards, the integral of 1/1-ax is (-1/a) ln |1-ax|. Knowing how that solve your problem without needing the calculator.

Switch_fx said:
Ok so this is my first post, and I am in dire need of assistance. I have a big exam tomorrow and if I can't figure out why my TI-89 is screwing up this simple integration I am in some trouble...

I am looking for the integral of : 1/[G-(Cv)/M] with respect to "v"

(erroneus, G=gravitational constant, C=drag coefficient, M=mass, and V=velocity)

anyways...
I know the correct answer is : -(M/C)[ln(G-(Cv)/M)]

but my TI-89 calculator gives back the answer as:

-(M/C)[ln(|Cv-GM|)]

If anyone could please explain to me why this is so or what I am doing wrong it would be of great help...and yes I am inputting the integral in the correct fashion

Thanks to anyone who can help!

~SWITCH

Take the "correct" answer, and use the logarithmic rule for division: ln(a/b) = ln(a) - ln(b). Normally I'd get in trouble for telling you that, but you could have just as easily looked it up in the textbook, so I thought I'd save you a couple minutes of tedious page turning. Anyway, considering what the others here have told you, just by expanding your answer in this way, you should be convinced that your answer and the 89's answer are the same.

## 1. What is the "TI-89 Titanium INTEGRATION Flaw"?

The "TI-89 Titanium INTEGRATION Flaw" refers to a software bug in the TI-89 Titanium calculator that causes it to give incorrect answers for certain integrals.

## 2. How does the "TI-89 Titanium INTEGRATION Flaw" affect calculations?

The flaw can cause the calculator to give incorrect answers for certain integrals, leading to incorrect solutions for math problems that involve integration. This can be especially problematic for students or professionals who heavily rely on the calculator for accurate calculations.

## 3. Are all "TI-89 Titanium" calculators affected by this flaw?

No, not all "TI-89 Titanium" calculators are affected by this flaw. It was reported that only some of the early models of this calculator are affected. However, it is always recommended to check for any software updates or patches from the manufacturer to ensure the calculator is functioning properly.

## 4. Is there a way to fix the "TI-89 Titanium INTEGRATION Flaw"?

Yes, there is a way to fix the flaw. Texas Instruments, the manufacturer of the calculator, has released a patch to fix this bug. Users can download and install the patch to resolve the issue and ensure the calculator is giving accurate results for integrals.

## 5. How can I prevent encountering the "TI-89 Titanium INTEGRATION Flaw"?

To prevent encountering the flaw, it is recommended to regularly check for software updates and patches from the manufacturer. Additionally, double-checking the results of any integral calculations on the calculator can help catch any potential errors caused by the flaw.