18.01SC | Fall 2010 | Undergraduate

# Single Variable Calculus

Part A: L'Hospital's Rule and Improper Integrals

## Session 91: Improper Integrals

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### Overview

Integration allows us to find the area under the curve. Improper integrals let us find this area (if it’s well defined) even when that curve extends to infinity. Knowing whether the area under a graph up to a large, finite value of x is significantly different from the area under the entire graph can help us simplify calculations and avoid approximation errors.

### Lecture Video and Notes

#### Video Excerpts

Clip 1: Introduction to Improper Integrals

Clip 2: Integral of e-kx

Clip 3: Integral of e-x2

Clip 4: Integral of 1/x

### Worked Example

Integrating 1/(5x + 2)2 from 1 to Inﬁnity

### Lecture Video and Notes

#### Video Excerpts

Clip 1: Integral of 1/(xp)

### Recitation Video

#### Improper Integrals

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## Course Info

Fall 2010
##### Learning Resource Types
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Simulations
Recitation Videos