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→Simpson's Rule: added a picture for example 2
=== Example 2 ===
=== Example 2 ===
Given:
Given:
: <math>\int_4^{12}\frac{3x+11}{x^2-x-6}dx </math>
: <math>\int_4^{12}\frac{3x+11}{x^2-x-6}dx </math>
:<math>a = 4</math>
:<math>a = 4</math>
:<math>b = 12</math>
:<math>b = 12</math>
{| class="wikitable" style="float: right"
|-
! <big>'''Example 2'''</big>
|-
|[[Image:Simpsonsrule3pc5.png|250px|Click on the image to get a better view.]]
|-
!width="250"|Explanation
|-
|This shows the parabolic approximation we are using. Note how much more error area that there is compared to the previous example.
|-
|}
:<math>f(x)=\frac{3x+11}{x^2-x-6}</math>
:<math>f(x)=\frac{3x+11}{x^2-x-6}</math>
:<math>f(4) = \frac{3(4)+11}{4^2-4-6} = {23 \over 6}</math>
:<math>f(4) = \frac{3(4)+11}{4^2-4-6} = {23 \over 6}</math>