3.7 The p-integral threshold · Techniques of Integration, Second Half · Visual Calculus

3.7p-integral threshold

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Chapter 2 · Applications of Integration

2.1-2.2Areas & Slicing

2.3-2.4Shells & Arc Length

2.5Physical Applications

2.6Centers of Mass

2.7-2.9Log, Exp & Hyperbolic

Chapter 3 · Techniques of Integration

3.1-3.4Techniques I

3.5-3.7Techniques II

3.5Strategy picker 3.6Numerical rules 3.7Infinite interval 3.7Gabriel's horn 3.7Vertical asymptote 3.7Interior singularity 3.7Comparison test 3.7p-integral threshold

Chapter 5 · Sequences and Series

5.1-5.3Sequences & Series I

5.4-5.6Sequences & Series II

Chapter 7 · Parametric Equations and Polar Coordinates

7.1-7.2Parametric Curves

7.3-7.4Polar Curves

Chapter 6 · Power Series

6.1-6.2Power Series I

6.3-6.4Power Series II

Home Calculus IISections 3.5-3.73.7 The p-integral threshold

3.7

The p-integral threshold

2

Interactive view

Previous · 3.7Compare to a known tail Next · 5.1An epsilon band makes convergence visible

Live setup

SymPy check = 1

SymPy checks

Revealed table-form area2.5548672746

Definite integral of e^(x^2)1.4626517459

Traffic tail probability0.0356739933

Gabriel's Horn volume3.1415926536

Endpoint singularity area4

Split convergent singularity area4

Convergent comparison bound0.3678794412

Convergent p-integral area1