18.01SC | Fall 2010 | Undergraduate

Single Variable Calculus

Part B: Partial Fractions, Integration by Parts, Arc Length, and Surface Area

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

Clip 1: Introduction to Integration by Parts

Recitation Video

Finding u and v’ When Integrating by Parts

Lecture Video and Notes

Video Excerpts

Clip 1: Integral of Natural Log

Clip 2: Integral of ln(x)2

Clip 3: A Reduction Formula

Clip 4: Another Reduction Formula

Recitation Video

Integrating sinn(x) Using Reduction

Worked Example

Integral of x4 cos(x)

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Course Info

Instructor
Departments
As Taught In
Fall 2010
Learning Resource Types
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Simulations
Recitation Videos