Approximate Integration is used when it is impossible or very difficult to find the exact value of a definate
integral.  This program uses 5 different techniques, Left Endpoint approximation, Right Endpoint approximation,
Midpoint Rule, Trapezodial Rule, and Simpsons Rules, to find aprroximate values for the definate integral.


How to use:


From the main menu select a rule you wish to use.

then enter the function that is inside of the integral. (you must use x as your variable)

enter the lower and upper limits that the integral is being evaluated for. (most books use 'a' to
refer to the lower limit and 'b' as the upper.)

enter the number of subintervals you want to use. (most books use 'n' to refer to subintervals)

the program will then return the answer.




********NOTE***********
*****When caluclating for high number of subinterval the program will take several seconds to return an answer.
1000 subintervals will take about 15 seconds on a ti-83 plus.

***** always use x as your variable

***** rembember that Simpsons rule only works for an even number of subintervals.

***** always quit by selecting quit since since the program needs to delete the varaiable it created which
can get very large if you use large subintervals.

**** when using trig functions make sure your calculator is in the correct mode.