Simpson’s rule allows approximate calculations of definite integrals that might otherwise not be easily calculable. The approximation is given by

wherethe number of strips, is even. Given an integral to estimate, we draw up a table of function values

Example: Using Simpson’s Rule with six strips, estimate the value of the integral

x-i |
0 |
1 |
2 |
3 |
4 |
5 |
6 |

f-i |
1 |
2 |
4 |
8 |
16 |
32 |
64 |

Example: Using Simpson’s Rule with five strips, estimate the to three decimal places the value of the integralFind the percentage error.

Because the final answer is to be to three decimal places, all figures in the working will be to four decimal places. Only the final answer will be to three decimal places.

x-i |
0 |
2 |
4 |
6 |
8 |
10 |
12 |

f-i |
0 |
1.4142 |
2 |
2.4495 |
2.8284 |
3.1623 |
3.4641 |

to four decimal places so

The true value is

The % error is