**Introduction**

This program computes left, right, Trapezoid, Midpoint, and
Simpson's approximations for
.

If you have not used one of the programs posted on this website before,
you should read through
the information in the Intro to Programming
section first.

**The Program **

:Prompt A,B,N | {Prompt is in PRGM under I/O} |

:(B-A)/NH | {The arrow is STO} |

:AX | {X is X,T button} |

:0L | {The 0 is a zero} |

:0M | {The 0 is a zero} |

:1J | {The 1 is a one} |

:Lbl 1 | {Lbl is in PRGM under CTL} |

:L+Y1*HL | {Y1 is in Y-VARS under FUNCTION} {The * is the times sign} |

:X+H/2X | |

:M+Y1*HM | |

:X+H/2X | |

:IS>(J,N) | {IS> is in PRGM under CTL} |

:Goto 1 | {Goto is in PRGM under CTL} |

:BX | |

:L+Y1*HR | |

:AX | |

:R-Y1*HR | |

:(L+R)/2T | |

:(2*M+T)/3S | |

:Disp "L R T M S" | {Disp is in PRGM under I/O} { " is on the + button} |

:Disp L | |

:Disp R | |

:Disp T | |

:Disp M | |

:Disp S |

**Running the Program**

You will need to enter a function *f*(*x*) into
Y1 before running
the program. The program will ask for values of A, B, and N (number of
subdivisions).

To test the program try the following:

*f*(*x*) = x^{2}+ 3,
A=1, B=4, N=20.

Your answer will be

L R T M S

28.88625

31.13625

30.01125

29.994375

30