**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.

If you have a TI Connectivity Cable, you can download the program main.allsums.89p

**The Program **
is STO}

:allsums( ) | {This will already appear if you named the program allsums} |

:Prgm | {This will already appear} |

:Clr IO | {Clr IO is in the CATALOG menu} |

:Lbl p | {Lbl is in the CATALOG menu} |

:Local a,b,n | {Local is in the F4 menu} |

:Input "a=", a | {Input is in the F3 menu} |

:Input "b=", b | |

:Input "n=", n | |

:(b-a)/nh | |

:ax | |

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

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

:For j,1,n | {For EndFor is in the F2 menu}{The 1 is a one} |

:l+y1(x)*hl | (The l is a lowercase L} {y1 is the Y button followed by a 1} |

:m+y1(x+h/2)*hm | {* is the times button} |

:x+hx | |

:EndFor | |

:l+y1(b)*hr | {The l is a lowercase L} |

:r-y1(a)*hr | |

:(l+r)/2t | {The l is a lowercase L} |

:(2*m+t)/3s | |

:Disp "L R T M S" | {Disp is in the F3 menu} |

:Disp l | (The l is a lowercase L} |

:Disp r | |

:Disp t | |

:Disp m | |

:Disp s | |

:Pause | {Pause is in the CATALOG menu} |

:Goto p | {Goto is in the CATALOG menu} |

:EndPrgm | {This will already appear} |

**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