Section 15.1 Double Integrals over Rectangles
- Volumes of Solids – The Main Idea
- Partial Integration & Iterated Integration
- Iterated Integral Example
- Fubini’s Theorem
- Average Value of a Function over a Rectangular Region
- Iterated Integral of a Product g(x)h(y)
Section 15.2 Double Integrals over General Regions
- Double Integrals over General Regions – The Main Idea
- Double Integral Setup with Two Regions
- Sketching a Region of Integration Example
- Volume of a Solid over a Triangular Region
- Volume of a Solid in the 1st Octant
- Properties of Double Integrals
Section 15.3 Double Integrals in Polar Coordinates
- Polar Areas using Double Integrals
- Double Integrals in Polar Coordinates
- Volume of a Solid using Polar Coordinates
- Volume of a Solid using Polar Coordinates – 2nd example
Section 15.4 Applications of Double Integrals
- Variable Densities and Centroids
- Moments of Inertia – The Main Idea
- Moments of Inertia – Basic Example
- Moment of Inertia Equilateral Triangle Example
- Integral Setup for Total Mass of Lamina
Section 15.5 Surface Area
Section 15.6 Triple Integrals
- Triple Integral Example
- Volumes Using Triple Integrals – The Main Idea
- Volume of Region Paraboloid Setup
- Volume of Solid Ex3
- Volume of Solid Ex4
- Volume of Solid Ex5
- Elliptic Paraboloid Triple Integral Setup
Section 15.7 Cylindrical Coordinates and Triple Integrals
- Cylindrical Coordinates – The Main Idea
- Converting a Triple Integral into a Cylindrical Coordinates
- Triple Integrals using Cylindrical Coordinates – Basic Example
- Volume of a Region Between Cylinders
Section 15.8 Spherical Coordinates and Triple Integrals
- Spherical Coordinates – The Main Idea
- Graphs using Spherical Coordinates
- Triple Integrals using Spherical Coordinates – The Main Idea
- Cone Inside a Cylinder Volume Example