2.3 Horizontal shells · Shells, Arc Length, and Surface Area · Visual Calculus

2.3Horizontal shells

∫Visual Calculus

Chapter 2 · Applications of Integration

2.1-2.2Areas & Slicing

2.3-2.4Shells & Arc Length

2.3Shell strips 2.3Shell accumulation 2.3Horizontal shells 2.3Shifted shell axis 2.3Shell height 2.3Shells vs washers 2.4Arc length in x 2.4Arc length in y 2.4Frustum bands 2.4Surface about y

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

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 2.3-2.42.3 Horizontal shells

2.3

Horizontal shells

Interactive view

3D shells

Previous · 2.3Shell accumulation Next · 2.3Shifted shell axis

Live setup

SymPy check = 160.8495438638

SymPy checks

Shell volume under 1/x12.5663706144

Shell volume under 2x - x^28.3775804096

Horizontal shell volume160.8495438638

Shifted-axis shell volume24.0855436775

Shell volume between curves59.0619418875

Method-choice comparison volume2.0943951024

Arc length y=f(x)2.2683538223

Arc length x=g(y)21.0277446726

Surface area around x-axis30.8464896971

Surface area around y-axis24.1179354649