Session 76: Integration by Parts

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Overview

Integration by parts is useful when the integrand is the product of an "easy" function and a "hard" one. In this session we see several applications of this technique; note that we may need to apply it more than once to get the answer we need.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Introduction to Integration by Parts (00:03:00)

» Accompanying Notes (PDF)

From Lecture 30 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

 

Finding u and v' When Integrating by Parts

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Lecture Video and Notes

Video Excerpts

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» Clip 1: Integral of Natural Log (00:03:00)

» Accompanying Notes (PDF)

From Lecture 30 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Integral of ln(x)2 (00:03:00)

» Accompanying Notes (PDF)

From Lecture 30 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 3: A Reduction Formula (00:06:00)

» Accompanying Notes (PDF)

From Lecture 30 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 4: Another Reduction Formula (00:07:00)

» Accompanying Notes (PDF)

From Lecture 30 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

 

Integrating sinn(x) Using Reduction

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Worked Example

 

Integral of x4 cos(x)

 

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