Chapter3 一元函数积分学

1不定积分

• 表格积分法原理

  \(\int udv\)

  \(---------------\)

  \(= uv - \int vdu\)

  \(= uv - \int u' d(\int v)\)

  \(= uv - [ u'(\int v) - \int (\int v) d u' ]\)

  \(---------------\)

  \(= uv - u'(\int v) + \int (\int v) du'\)

  \(= uv - u'(\int v) + \int u'' d( \int \int v)\)

  \(= uv - u'(\int v) + [ u''(\int\int v) - \int (\int\int v) du'']\)

  \(---------------\)

  \(= uv - u'(\int v) + u''(\int\int v) - \int (\int\int v) du''\)

  \(= uv - u'(\int v) + u''(\int\int v) - \int u''' d( \int\int\int v)\)

  \(= uv - u'(\int v) + u''(\int\int v) - [ u'''(\int\int\int v) - \int (\int\int\int v) du''' ]\)

2定积分

3反常积分

4定积分应用