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→Example 1: added further explanations
<br />Now we can evaluate the integral:
<br />Now we can evaluate the integral:
:<math>{{4-1} \over 6} \left [ 3 + 4(7.875) - 3 \right ] = \left ({1 \over 2} \right)(31.5) = 15.75</math>
:<math>{{4-1} \over 6} \left [ 3 + 4(7.875) - 3 \right ] = \left ({1 \over 2} \right)(31.5) = 15.75</math>
In the picture on the right the "error area" is the yellow and dark red area. In cases where the approximation does not give a good answer, we increase the number of subintervals.
If we solve this using [[integration]], we find that Simpson's Rule gave the '''exact''' value for the definite integral. ''However, this is rarely the case'', as shown in the next example.
If we solve this using [[integration]], we find that Simpson's Rule gave the '''exact''' value for the definite integral. ''However, this is rarely the case'', as shown in the next example.