Evaluating Definite Integrals: TI83

• There are two common methods for the evaluation of a definite integral f(x) dx using a TI83.  They are as follows:
  
  
  1. Graphically.  This method illustrates the computation of the definite integral by means of finding areas of the regions between the curve y = f(x) and the x-axis, with areas of the regions above the x-axis counted positively, and areas of the regions below the x-axis counted negatively.
     
     
     1. First graph y = f(x) on some interval that contains a x b.  (It seems that this method of evaluation can be applied without any of the region actually being visible in the graphing screen, but we recommend that the graphing window is arranged so that the entire region between the curve y = f(x) and the x-axis is visible.)
        
        
     2. Once you have the graph, go to [2nd][TRACE] (which is [CALC]) and select option 7:§f(x)dx.
        
        
     3. At the bottom of the screen, the calculator will ask ``Lower Limit?'', for which you respond with the value of a (and press [ENTER]).  The calculator will then ask ``Upper Limit?'', for which you respond with the value of b (and press [ENTER]).
        
        
     4. The corresponding regions between the graph of y = f(x) and the x-axis will be shaded in, and a numerical approximation of the definite integral will be given at the bottom of the screen.
        
     
     
  2. Built-in function.  This method is fairly straight-forward, and is equivalent to providing the integrand and the limits of integration for a computational package that will, in turn, provide a numerical approximation of a definite integral.
     
     
     1. Go to [MATH] and select option 9:fnInt(.  Note that this option will not be immediately visible on the screen, and you must scroll down the list of options in order to see it.  At this selection, the command fnInt( will appear on the command screen.
        
        
     2. Now complete this command by typing in what remains of the expression ``fnInt(f(x),x,a,b)''.  You will have to type in the actual function f(x), the variable x that the calculator is using (press the [X,T,,n] key), and then the actual values of a and b, with each input separated by commas, and closed with a right parenthesis.  Then press [ENTER].
        
        
     3. A numerical approximation of the definite integral will then be given on the next command line.
        
        
  
  

---

Last modified: Wed Apr 24 2002