Changes

:<math>\left ({12-4 \over 6}\right ) \left ( {23 \over 6} + 4 \left( {7\over10} \right)+ {47 \over 126} \right ) = \left ( {4\over3} \right ) ({2207\over315}) \approx 9.34179... </math>

:<math>\left ({12-4 \over 6}\right ) \left ( {23 \over 6} + 4 \left( {7\over10} \right)+ {47 \over 126} \right ) = \left ( {4\over3} \right ) ({2207\over315}) \approx 9.34179... </math>

<br />As the function given does not resemble a parabola, the answer we get is completely off of the real answer, which is:

<br />As the function given does not resemble a parabola, the answer we get is completely off of the real answer, which is:

: <math>\approx 6.02941...</math>

: <math>\approx 7.94160...</math>

This is why we will sometimes split the interval of integration into multiple pieces, causing the approximation to approach the actual value. When we do this, we use the '''Composite Simpson's Rule'''.

This is why we will sometimes split the interval of integration into multiple pieces, causing the approximation to approach the actual value. When we do this, we use the '''Composite Simpson's Rule'''.