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MA35 Labs

1 Single Variable Calculus

2 » Two Variable Calculus

3 Three Variable Calculus

Polar Coordinate Labs

Two Variable Functions

Contents

2.1 Functions of Two Variables

2.2 Differentiation

2.3 More Derivatives

2.4 Integration

2.4.1 Volume Under a Function Graph

2.4.2 Riemann Integral

2.4.3 Volume between Function Graphs

2.4.4 Change of Order of Integration

2.4.5 Surface Area for Function Graphs

2.4.6 Change of Variables

2.4.7 Total Mass of a Region in the Plane

2.4.8 Center of Mass

2.4.9 Moment of Inertia

2.5 Vector Analysis

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Total Mass of a Region in the Plane (Page: 1 | 2 )

Text

The mass of an object is calculated by integrating its density function over the region of the domain that it occupies. For a density function ρ(r,θ) of two variables and an object in the domain of ρ occupying a region R, the mass is ∫∫_Rρ(r,θ) rdrdθ.

Demos

Density Functions and Mass
	This demo resembles that on page 1 except that the domain is given in polar coordinates.