Integrating multivariable functions videos

Introduction to the line integral

Line integral example 2 (part 1)

Line integral example 1

Line integral example 2 (part 2)

Line integrals and vector fields

Parametrization of a reverse path

Using a line integral to find work

Scalar field line integral independent of path direction

Vector field line integrals dependent on path direction

Path independence for line integrals

Closed curve line integrals of conservative vector fields

Example of closed line integral of conservative field

Second example of line integral of conservative vector field

Double integral 1

Double integrals 2

Double integrals 3

Double integrals 4

Double integrals 5

Double integrals 6

Polar coordinates

Triple integrals 1

Triple integrals 2

Triple integrals 3

Parametrizing a surface, part 1

Determining a position vector-valued function for a parametrization of two parameters

Partial derivatives of vector-valued functions

Introduction to the surface integral

Example of calculating a surface integral part 2

Example of calculating a surface integral part 1

Example of calculating a surface integral part 3

Surface integral example, part 1

Surface integral example part 2

Surface integral example part 3: The home stretch

Surface integral ex2 part 1

Surface integral ex2 part 2

Surface integral ex3 part 3

Surface integral ex3 part 1

Surface integral ex3 part 2

Surface integral ex3 part 4

Constructing a unit normal vector

Conceptual understanding of flux

Vector representation of a surface integral