18.01SC | Fall 2010 | Undergraduate

Single Variable Calculus

Part C: Mean Value Theorem, Antiderivatives and Differential Equations

Session 38: Integration by Substitution

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When asked to find the antiderivative of an expression involving familiar functions, we often have an idea of what the answer might be. We can then check and correct our guess by taking the derivative. This “advanced guessing” is related to the technique called “substitution”, in which we attempt to simplify the integrand as a step toward finding the derivative.

Lecture Video and Notes

Video Excerpts

Clip 1: Substitution

Clip 2: Integration by “Advanced Guessing”

Clip 3: More Examples of Integration

Recitation Video

Antidifferentiation by Substitution

Worked Example

Antiderivative of tan x sec2x

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Course Info

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