September 25, 2009
No CommentsUsing Simpson’s Rule to Solve Error Bounds
Description
A detailed tutorial on using Simpson’s rule and solving error bounds. Step by step tutorial including examples of solving error bounds using Simpson’s rule for reference.
Overview
Simpson’s rule is a rule in calculus that is used to solve error bounds. It is the more complicated form of both the trapezoidal rule and the midpoint rule, both of which are also used to calculate error bounds. Although this rule is harder to use than either one of those, it is more accurate. The Simpson’s rule does not use anything except for numbers to calculate the space under a graph, and is expressed by this formula:
![\int_{a}^{b} f(x) \, dx \approx \frac{b-a}{6}\left[f(a) + 4f\left(\frac{a+b}{2}\right)+f(b)\right]](http://s.wordpress.com/latex.php?latex=%20%5Cint_%7Ba%7D%5E%7Bb%7D%20f%28x%29%20%5C%2C%20dx%20%5Capprox%20%5Cfrac%7Bb-a%7D%7B6%7D%5Cleft%5Bf%28a%29%20%2B%204f%5Cleft%28%5Cfrac%7Ba%2Bb%7D%7B2%7D%5Cright%29%2Bf%28b%29%5Cright%5D&bg=ffffff&fg=000000&s=0 "\int_{a}^{b} f(x) \, dx \approx \frac{b-a}{6}\left[f(a) + 4f\left(\frac{a+b}{2}\right)+f(b)\right]")
