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Mathematics how to solve integration of exp^x square with lower limit=0 and upper limit=infinity

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  • Ronald Tisdale
    Ronald Tisdale May 11, 2010

    prove that the integral of exp(-x^2) from zero to infinity = square root of pi??



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Drag the red point. at link below

The following program computes exp(x) for an input x using the
! infinite series of exp(x). This program adds the
! terms together until a term is less than a specified
! tolerance value. Thus, two values are required:
! the value for x and a tolerance value. In this program,
! he tolerance value is set to 0.00001 using PARAMETER.

Posted on May 06, 2008


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Well..first thing I'd do, is pour a tall cold one, and ponder the importance of this equation..then I'd navigate my belly button with my fingers, and in that process, enlightenment would arise, with the proper Fixya Solution set, no?

Posted on May 05, 2008


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Hi, How do i find the upper bound on a casio calculator when the lower bound, the function and the area (integration value) are given?

Let us consider this to be math problem. From the physics point of view the units are inconsistent:thus the problem is ill-posed.
What you need it to draw the graph pf the function y=cos(t^2), then the integration feature of the calculator to calculate the integral between 0 and some upper limit, which will be found by trial and error.
Here are some screen capture to help you along the wayimage 1-kgpayaan5mwqlexbne0izpdg-2-0.jpg
Make sure the graph type is y=cos(X^2). Don<t worry the variable in this type of graph must be Ximage 2-kgpayaan5mwqlexbne0izpdg-2-1.jpg
Choose the window to start at x=0image 3-kgpayaan5mwqlexbne0izpdg-2-3.jpg

Here is your graph.
image 4-kgpayaan5mwqlexbne0izpdg-2-6.jpg
Press SHIFT F5 (G-Solv) You see the following image
image 5-kgpayaan5mwqlexbne0izpdg-2-10.jpg
Press F6 (Arrow pointing right) to access the other features, as on the following screen:
image 6-kgpayaan5mwqlexbne0izpdg-2-21.jpg
You see the integral sign above F3: Press F3 to do integration.

image 7-kgpayaan5mwqlexbne0izpdg-2-28.jpg
Use the left Arrow key to move the cross on the graph to X-0 or just enter 0. and press EXE. This is the lower bound.
image 8-kgpayaan5mwqlexbne0izpdg-2-36.jpg
You need to enter the upper bound. Since you do not know where to stop you must try different values and each time, read the value of the integral. For example if you enter Xupperlimit=0.5image 9-kgpayaan5mwqlexbne0izpdg-2-45.jpg
the value of the integral is 0.45 (not 1)image 10-kgpayaan5mwqlexbne0izpdg-2-55.jpg
Repeat the process changing the upper limit until (if you are lucky) you hit an integral of 1.
Now a few more pictures

image 11-kgpayaan5mwqlexbne0izpdg-2-66.jpg
image 12-kgpayaan5mwqlexbne0izpdg-2-78.jpg

image 13-kgpayaan5mwqlexbne0izpdg-2-91.jpg
Getting close. Now I use the 1st zero of the function, x=1.2533 approximate
image 14-kgpayaan5mwqlexbne0izpdg-2-105.jpg
Getting close. However from that zero to the next the area under the curve under the x-axis is negative and there will not be a solution until maybe somewhere in the second positive part.
So you can accept the value of the integral from X=0 to the 1st zero (1.2533) to be about 1. Or you will keep playing the game. But as the next picture shows, you will not get a better approximation than at the first zero.

image 15-kgpayaan5mwqlexbne0izpdg-2-120.jpg

Good Luck.

Oct 12, 2016 | Casio Fx-9860gii Graphing Calculator

1 Answer


The calculator does not have a CAS, no need to bother about infinity. If you have to do some integral, it a must be a definite one, ie with fixed lower and upper bound.

Apr 16, 2014 | Casio FX-270W Calculator

1 Answer

Integrate equations, using 0 and .123 as limits

Set Input/output to MathIO.
Press the Integrate key, to the right of CALC.
The image of integral appears with a rectangle for the function, and two small squares (one for the upper limit the other for the lower limit).


Type in the integrand (the expression you want to integrate) in the bigger (on your display) rectangle. Use appropriate parenthesis. To type in X press [ALPHA] )
Use the down arrow to move cursor to the square for the lower limit. Type in the lower limit. Use the Up arrow to move cursor to the upper limit square. enter the upper limit. Press [=] key. If you did not make mistakes, and your expression is not too complicated you should get your integral.


Note: The screen captures are not from a Casio FX991ES. But that should not matter to you.

Feb 10, 2014 | Casio FX991ES Scientific Calculator

1 Answer

How to solve definite integrals between two limits

To calculate the definite integral (integral with specified lower and upper bounds)
  1. In Run/Math screen press OPTN
  2. Press F4:CALC
  3. Press F4:$ (integral)
  4. After the $( type in the function of X, enter comma, enter the lower bound, comma, upper bound, right parenthesis to close.
  5. Press =

Another way is to graph the function. While graph is displayed press SHIFT: F5:G-Solve, then F6>, Then F3:$(
Use arrow key to select the lower bound, then select select the upper bound. Press = to get result. The area concerned will appear shaded.
Note: There is a drawback to this method. The lower and upper limits must be inside the graph window limits.

Apr 30, 2012 | Casio FX-9860G Graphic Calculator

1 Answer

How can i solve integrals with ALGEBRA FX 2.0 PLUS

The syntax for the evaluation of definite integrals (integrals with boundary limits) is as shown on the screen capture below.

$ (function , variable , lower bound, upper bound)
By default the name of the dummy variable is x. If you use another name, the variable must appear as an argument of the function, and as variable.


Mar 13, 2012 | Casio Algebra FX 2.0 Calculator

1 Answer

How to calculate a finite integral

Press 2ND MATH to bring up the Math menu. Select "Calculus" and then "integrate." Enter the expression, the variable of integration, the lower limit, and the upper limit, separated by commas. Close the final paren and press ENTER or diamond ENTER.

For example, to calculate the integral from 0 to pi of sin(x) dx, you want


where INT is the integral sign and pi is the lower-case Greek pi.

Sep 22, 2010 | Texas Instruments TI-89 Calculator

1 Answer

Integral of sinx how to calculte in casio fx991 es

Configure the calculator to be in MathIO : [SHIFT][MODE][1:MathIO].
Press the Integral key, the one judt beloe the [ALPHA] key.
The template of the integral appears, with the cursor in larger rectangle. Enter the function the screen displays the integral, a small upper sqaure, and a small lower square. The left parenthesis of the function is already supplied by the calculator.
Press [ALPHA] X to enter the argument of the function.
Press the right parenthesis.
Remain the limits.
Use left arrow to move the cursor just before the s of sin and press down arrow to enter a numerical value for the lower limit.
Press the up arrow to move cursor in upper square.
Key in the numerical value of the upper limit.
Press [=].

Warning. To have meaningful result, make sure the angle unit used is conform to the problem you are trying to solve.

Hope it helps.

Nov 01, 2009 | Casio FX-300MS Calculator

1 Answer

How do i use the solve( function

The solve( is available through the CATALOG : [2nd][CATALOG], scroll down till you reach the command. Highlight it and press [ENTER]. The command echodes on main screen as solve( .
You complete the command by entering the expression (not the equation), the name of the variable you solve for, the initial guess , and { lower limit, upper limit} between curly brackets, and the closing parenthesis.
solve ( Q^3-100, Q,0 {-50,50} ) [ENTER]
It is implied that the expression is 0 (Q^3-100 =0), so you should not insert =0, otherwise you get an error. Here the lower limit is -50. You must use the change sign symbol (-) under the 3 key, not the regular MINUS.
Hope it helps.


Oct 14, 2009 | Texas Instruments TI-83 Plus Calculator

2 Answers

Integration with limits & with out limits

This calculator can only perform NUMERICAL DEFINITE integrals. Which meansyou have to supply the numerical value of the lower limit and the numerical value of the upper limit. The result is a numerical value.
The calculator cannot perform symbolic calculus.

If the function is simple you find the integral in tables of integrals where you will see that INT(log(X)dx=x(log(x)+1). Some calculators that have a CAS (computer algebra system) can manipulate symbolic expression, but not theCasio FX-991ES.

You ask it the value of the integral of log(X) from X=1 to X=3 and it will give you 0.5627748004

Hope it helps

Dec 12, 2008 | Texas Instruments TI-84 Plus Calculator

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