Question about Texas Instruments TI-84 Plus Silver Edition Graphic Calculator

# Finding a limit "a" on an integral with a fixed area

TI-84 Plus Silver Edition Graphing Calculator Question: I have an integral from 0 to a, and I need to find the value of a for which the integral equals 1. How do I find this with my graphing calculator?

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• Texas Instru... Master

There are several ways of doing this.

Since you're using a graphing calculator, you can always graph it as a function of 'a' and use the graphical tools.

Another way is to use the solve() function. For example, to find the value of a where the integral of sin(x) from 0 to a equals one, enter
solve(fnInt(sin(X),X,0,A)-1),A,1.5)

solve( and fnInt( are accessible through the CATALOG. The 1.5 is an initial guess.

Posted on Apr 19, 2014

Testimonial: "Thanks for the help! I've tried the Solve suggestion (as I don't know how to find it by graphing) but when I try to solve for A the calculator responds with ERR:SYNTAX and brings me back to the comma before the last A in the eqn :("

• kakima Apr 21, 2014

Sorry, there is a typo in what I gave you. It should be solve(fnInt(sin(X),X,0,A)-1,A,1.5) There is an an extra ")" just before the final "A".

• Caroline Kolln Apr 22, 2014

OMG YES. :D :D :D Thank you so much!!!! It now still brings me back to that comma (I just inserted the "(" keeping everything else the same). I deleted that comma but it brought me back to the comma between the final A and 1.5. I deleted that, then brought me back to the last ")". Deleted that. Then it worked.

• Caroline Kolln Apr 22, 2014

Wait. I'm trying it for cos(x^2) from 0 to A with an area of 1.

• Caroline Kolln Apr 22, 2014

Nvm works ^.^

• kakima Apr 22, 2014

That's impossible. The maximum value of the integral of cos(x^2) from 0 to a is about 0.977 at a=sqrt(pi/2).

• Caroline Kolln Apr 22, 2014

It's absolute value of cos(x^2), so the graph doesn't go under the x-axis and therefore can have an infinite area.

• Caroline Kolln Apr 22, 2014

I neglected to mention that my b

• kakima Apr 22, 2014

Yes, the absolute value would make a difference. solve(fnInt(abs(cos(X^2)),X,0,A)-1,A,1.2)

• kakima Apr 22, 2014

With the above, I get about 1.3858. Be patient, it takes about 35 seconds.

• Caroline Kolln Apr 22, 2014

Yay that's correct. Thank you :D

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• Texas Instru... Master

Here is an example using an integrand of (1-X^2). For the explanation see another expert's answer.The screen capture shows the whole entry line (with a result in the middle). If your calculator does not show the integral template, upgrade it to the latest OS version.

The integral as a function of A is equal to
A-(1/3)A^3
Using the approximate result obtained above you see that the result is very close to 1. The result is exactly 1 but I would not take it at face value because of rounding errors.

Posted on Apr 20, 2014

Testimonial: "Thanks for the help! Erm, how did you access that integral on your calculator? I'm not sure if I have it."

• k24674 Apr 20, 2014

The last argument of the solve( utility is the initial guess, to accelerate the search of the solution.

• k24674 Apr 21, 2014

I told you if you do not have the integral template, you should upgrade the OS version to the latest one maybe 2.54 or 2.55 MP. It is available on the education.ti.com website>latest OS

• k24674 Apr 21, 2014

If the display mode (MODE button) is set to CLASSIC you will not have the template. You should select MATHPRINT. To get it press MODE, then scroll down till you reach the second page.

• Caroline Kolln Apr 22, 2014

I don't have a second page on mode. Ok I'll check that out. Thank youu!!

• k24674 Apr 22, 2014

Upgrade to OS 2.55MP. Press MODE, you get the first configuration screen. Scroll to reach NEXT. The first line of second page (at the top it has BACK) shows t on the line MATHPRINT and CLASSIC. Select Mathprint. Press MATH key then 9:fnInt(

• Caroline Kolln Apr 23, 2014

ok thanks :)

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Posted on Jan 02, 2017

My screen was frozen and I needed to do a manual reset. If you take out 1 battery from the back....hold the "del" key down and reinsert the battery while holding it down....it will reload the programming into the calc

Posted on Aug 25, 2008

"2nd" + "log"

Posted on Jun 07, 2009

Hi persaud sabr,

Make sure the batteries are in correctly? The batteries alternate negative/positive, positive/ negative and so on. The first time I put the batteries in, I didn't have them in correctly. I know if it happen to me anybody could make the same mistake. and of course the calculator will never come on if the batteries aren't in correctly.

The process below should reset your calculator.

Please be prepared to re-install the calculator's OS if you run through this process.

Press and release the 2ND key. Press and hold the Up-arrow key for a few seconds. Now, Pressing the [2nd] key followed by pressing and releasing the up arrow; repeat as necessary. Is the screen showing any activity? If not continue the process.

1. Remove one of the AAA batteries. Press and hold the [CLEAR] key. While holding [CLEAR],
reinsert the AAA battery and then turn the calculator on. The calculator should display the
message "RAM Cleared". Release the [CLEAR] key and then press it one more time to remove the message. If calculator did not display the message try pressing and releasing the [2nd] key followed by pressing and releasing the up arrow for one second. goto step 2.
2. Remove one of the AAA batteries. Press and hold the [DEL] key. While holding [DEL], reinsert the AAA battery and then turn the calculator on. The calculator should display
TI-83 family or TI-84 Plus family to reinstall the calculator operating system. If the calculator did not turn on connect the calculator to the computer and open Ti Connect. Next, open Device Explorer. Is the calculator asking to be installed? goto step 3.
3. Steps to re-installing the operating system:

~Connect the TI Connectivity cable between the PC and the calculator.
~Click on Start >> Programs >> TI Tools >> TI Connect >> TI OSDownloader
~Follow the on-screen directions to reinstall the calculator's OS. When or, if the calculator install the fresh OS goto step 4.

4. Remove all of the batteries including the round lithium battery for 5 minutes. After the 5 minute period, reinsert all of the batteries and turn the calculator on. Adjust the contrast if necessary.

If the above process did not work. Try re-doing the procedure and, extend the time in step 4 by 5 minutes to 10 minutes before you put all the batteries back in the calculator.

Posted on Jan 04, 2011

Change the battery

Posted on Apr 07, 2011

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The illustration and solution are courtesy of Jesse Phillips, who cites this page from the Texas Instruments support site

- doug garfinkel, Children's Day School

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