• 2022-06-09
    试导出三重积分的梯形公式和辛卜生公式。
  • 解: 设[tex=16.071x1.357]e5LW61vmiIO7L/pSOctko8yKP2IYRJJaMm6njgQuv9R7+H5dvt/41k6MgRhYuCj31TYBTV0HeUYQ5sBv1w3n+FnlNKOdifMfW29fAWbie74=[/tex], 则三重积分的梯形公式和辛卜生公式分别为:[tex=28.214x4.214]ifE9NWj3X6IpRVSt3T5ITpDmDm3mZVsQnDIR80NejOpQx+9hspbNTSDfDdDer7LxlYTjh54vJJo/Ut2P04O5ej5dUspWyx2jRwhI6OZ/TqmJC7PtS+fV/87pS1Uu9C7nUs8igHqgHde/kjclA1Lz7YwPWdcm/Fe4mMQHkRd095j68vmiTYFA7vTerULRcagUZQ/BX7RcQTK7LKCRU0Kp7iotWmkoxKkjwwUfQ3SpX6w=[/tex][tex=33.643x14.357]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[/tex][tex=24.857x11.286]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[/tex]

    内容

    • 0

      分别用复化梯形公式和复化辛卜生公式按 [tex=0.5x1.0]rKFFlF9QyjLaLZIVnZoUfQ==[/tex] 位小数计算积分[tex=4.429x2.786]/CYoxXxOdWOSL/9kQ8/y+qMHm1qbkYGmqKTZI5ym5nIVzuswX4ob/ZQWHwgYyOoh[/tex],取 [tex=1.929x1.0]au2olChJIABR52MosDCmMw==[/tex],并与精确值比较,指出各有几位有效数字。

    • 1

      证明梯形求积公式的代数精度为1,辛浦生求积公式的代数精度为3.

    • 2

      验证复化柯特斯公式和复化辛卜生公式之间存在递推关系[tex=6.571x2.429]VbmRrPYmjAXJEn5vT/kwCJ1+eNrKdaEvpka0/jK6KiWsIxTnhqKsq7dd0/cL8+gU[/tex]

    • 3

      利用(52)式推导当[tex=1.929x1.0]NmPA2D71I8nc/KlCSQGiHQ==[/tex]时的三角辛卜生公式。

    • 4

      试从[tex=0.5x1.0]kWHXnAmgtG5MYBG1PDb4lg==[/tex]函数的线积分表示导出拉普拉斯逆变换公式.