Midpoint Derivative-Based Closed Newton-Cotes Quadrature

<table class="table-group" id="tab10"><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">8.3890560989</td><td align="center">2.0000000000</td><td align="center">6.5768682133</td><td align="center">0.1878121144</td></tr><tr><td align="left">2</td><td align="center">6.9128098779</td><td align="center">0.5237537790</td><td align="center">6.4019423495</td><td align="center">0.0128862506</td></tr><tr><td align="left">4</td><td align="center">6.5216101094</td><td align="center">0.1325540105</td><td align="center">6.3898812442</td><td align="center">0.0008251453</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 10