Integration using a TI-89 produces wrong value?

[vnaut]

Hi Physics Forum,

I've just started taking Diff EQ and have been using my calculator for most integrations. I've come across two problems that I hope have answers.

1) When I try the integral of (x+1) (the quantity! not just x+1), my calculator still spits out (x^2/2)+x while the real answer should be (-(x+1)^2)/2. Is there a way to make my calculator identify (x+1) as the quantity (or is it factor? I forgot the actual term) rather than just x+1?

2) When I integrate 3/(100+2*x) I'm getting 3/2 * ln(x+50). However, I'm 99% sure the answer should be 3/2 * ln(100+2x). What am I/the calculator doing wrong?

Any and all answers are appreciated, thanks so much!

 

[Borek]

$$\frac 3 {100+2x} = \frac 3 {2(50+x)}$$

 

[vnaut]

$$\frac 3 {100+2x} = \frac 3 {2(50+x)}$$

This is where I'm confused. Multiple integral tables say that that

the integral of 1/(ax+c) is (1/a) * ln(ax+c). This would yield 3/2 * ln(100+2*x) where as the integral of your answer would yield 3/2 * ln(50+x). So I'm left with two different answers to choose from.

Either 3/2 * ln(100+2*x) or 3/2 * ln(50+x). Very curious =x

 

[AlephZero]

In both your examples, the difference in the "answers" is just a constant, so you can think of it as part of the arbitrary constant in an indefinite integral.

If you are going to evaluate a definite integral, the arbitrary constant cancels out so it doesn't matter.

In the first example the difference is the constant 1/2.

In the second example, from the properties of logarithms,
log(100 +2x) = log(2(50 + x)) = log(50+x) + log 2.

 

[LudusRex]

Hello,

Thank you for reaching out with your questions. It seems like you may be experiencing some errors with your TI-89 calculator when it comes to integration. I have a few suggestions that may help you troubleshoot and find the correct answers.

Firstly, it is important to make sure that your calculator is set to the correct mode for integration. This can usually be found in the settings or mode menu. You may need to switch between Radian mode and Degree mode, depending on the type of problem you are working on. Double check that you are in the correct mode for the problem you are trying to solve.

Next, when using the TI-89 for integration, it is important to use the correct syntax. For example, to integrate (x+1) you would enter "int(x+1,x)" and for 3/(100+2x) you would enter "int(3/(100+2x),x)". Make sure you are using parentheses correctly and using the correct variables for your problem.

If you are still getting incorrect answers, it may be helpful to double check your work by hand or using another calculator. If the problem persists, you may need to reset your calculator or seek assistance from the manufacturer.

I hope this helps and good luck with your studies in Differential Equations!