Midpoint Derivative-Based Closed Newton-Cotes Quadrature

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left" rowspan="2">Int.</td><td align="center" colspan="2">Trapezoidal rule</td><td align="center" colspan="2">Midpoint derivative Trapezoidal rule</td></tr><tr class="thead"><td align="center">Approximate value</td><td align="center">Error</td><td align="center">Approximate value</td><td align="center">Error</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">1</td><td align="center">3</td><td align="center">0.1415926536</td><td align="center">3.0853333333</td><td align="center">0.0562593203</td></tr><tr><td align="left">2</td><td align="center">3.1</td><td align="center">0.0415926536</td><td align="center">3.1414302104</td><td align="center">0.0001624432</td></tr><tr><td align="left">4</td><td align="center">3.1311764706</td><td align="center">0.0104161830</td><td align="center">3.1415916562</td><td align="center">0.0000009974</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

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Abstract and Applied Analysis

Midpoint Derivative-Based Closed Newton-Cotes Quadrature

Table 6