To use this applet, do the following:

1. Enter an equation of the form y = f(x) into the equation box.
   
   Valid operators include: +, -, *, /, and ^. Parentheses may be used for grouping.
   Valid functions of x include: abs(), acos(), asin(), atan(), cos(), exp(), int(), ln(), log(), sin(), sqr(), sqrt(), and tan().
   
   
2. Enter starting and ending values for x into the x0 and xn boxes.
   
   
3. Enter the number of integration intervals into the # intervals box.
   
   
4. Choose the desired shading for the graph by checking one of the five radio buttons.
   
   
5. Click the "Evaluate" button. If there is a syntax error, then you will receive a message to that effect in the "Syntax Check" box. Otherwise, the graph of the equation will be displayed, and the values of the trapezoid, Simpson, left endpoint, midpoint and right endpoint approximations will be shown to the right of the graph. The graph will be shaded in accordance with the checked radio button. If desired, you can use the radio buttons to change the shading after the graph is displayed.
   
   Note: Simpson's rule requires an even number of intervals. If the number of intervals entered is odd, then no value will be given for the Simpson approximation, and if the Simpson radio button is checked, then no shading will be shown.
   
   
6. If the program encounters a division by zero or some other operation that fails to produce a number, then it will respond with the symbol NaN (Java's designation for "Not a Number").