# Difference between revisions of "Math 22 Integration by Parts and Present Value"

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## Revision as of 16:21, 3 September 2020

## Integration by Parts

Let and be differentiable functions of .

**Exercises** Use integration by parts to evaluation:

**1)**

Solution: |
---|

Let , |

and and |

Then, by integration by parts: |

**2)**

Solution: |
---|

Let , |

and and |

Then, by integration by parts: |

**3)**

Solution: |
---|

Let , |

and and |

Then, by integration by parts: |

Now, we apply integration by parts the second time for |

Let , |

and and |

So |

Therefore, |

## Note

1. Tabular method is convenient in some cases.

**This page were made by Tri Phan**