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

Recitation Video

A Solid With Finite Volume and Infinite Cross Section

Lecture Video and Notes

Video Excerpts

Clip 1: Integral of 1/(xp)

Recitation Video

Improper Integrals

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Course Info

Learning Resource Types

grading Exams with Solutions
notes Lecture Notes
theaters Lecture Videos
assignment_turned_in Problem Sets with Solutions
laptop_windows Simulations