Make sure you have derived the results from 'Towards Simpson's Rule'. [url]http://www.geogebratube.org/student/m56927[/url] The blue dots represent [math]\left \{ y_0,y_2,y_4,\ldots,y_n\right \}[/math]. The pink dots represent [math]\left \{ y_1,y_3,y_5,\ldots,y_{n-1}\right \}[/math]. You can change the function, move the red dots to change the upper and lower limits of the integration. You can also change the number of intervals. For clarity, only the first two parabolic approximations are shown. [b]Task 4:[/b] See how the increasing the number of intervals increases the accuracy. Can you find an integral where the accuracy isn't very good? [b]Task 5:[/b] Show that [math]\displaystyle \int_a^b \mbox{f}(x) \mbox{ d}x \approx \frac h 3 \left[ y_0 + y_n + 4\left( y_1+y_3 +\ldots +y_{n-1}\right)+2\left( y_2+y_4 +\ldots +y_{n-2}\right)\right] [/math].
Created by Dr GJ Daniels.