## The Mid Ordinate Rule

Also called the midpoint rule – the mid ordinate rule is another method to numerically estimate integrals. It states:

If an area of integration is divided into n strips, the area of the strip betweenandis given byso that the width of the strip is multiplied by the– value at the midpoint.

We do this for all n strips obtainingIf the strips are all of the same widthwhereandare the limits of integration, then we can write,

Example: Using the mid ordinate rule with 5 strips, estimate the vale of the integralto three decimal places. Evaluate the integral and compare the approximation given by the ordinate rule with the true value.

Complete the table of values forSince we must estimate the value of the integral to three decimal places, we calculate values to four decimal places. The final answer is quoted to three decimal places.

I | 0 | 1 | 2 | 3 | 4 | 5 |

0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 | |

0.1 | 0.3 | 0.5 | 0.7 | 0.9 | ||

1.1052 | 1.3499 | 1.6487 | 2.0138 | 2.4596 |

The % error is