Background

When might we need to evaluate an integral with data?

Numerical routine to integrate two functions and find a centroid - Magrab p. 154 (uses quadc() routine)

Expectations:

PowerPoint Problem Setup

Explanation of numerical integration background, equation derivation

Cover the questions

Cover strategy, writing out what to do before implementing, how to implement in a spreadsheet

Spend a day working in a computer lab

Simpson's Rule to approximate the integral of a function,

$I = int_{a}^{b} f(x) dx$

We can approximate this by splitting up the interval into sub-intervals, constructing strips, and approximating the area of each strip

Chapter 5, first introduction to integration: we explored the left-hand, right-hand, and midpoint rules.

These use a constant function. 1 parameter, 1 function evaluation.

Trapezoid rule: extends the technique by approximating with a line. 2 parameters, 2 function evaluations. 1 rectangle strip.

$A = \Delta x \left( \frac{1}{2} y_0 + y_1 + y_2 + \dots + y_{N-1} + \frac{1}{2} y_{N} \right)$

Simpson's Rule: extension to quadratic polynomial approximation. 3 parameters, 3 function evaluations. 2 rectangle strips.

$$ a+b $$