Applications of Integration
Apply integration to compute areas, volumes, arc length, surface area, centers of mass, work, and exponential models.
Areas between curves, volumes by slicing and shells, arc length and surface area, moments, exponential and hyperbolic functions
Area of a Region between Two Curves
Areas of Compound Regions
Regions Defined with Respect to y
Volume and the Slicing Method
Solids of Revolution
The Disk Method
The Washer Method
The Method of Cylindrical Shells
Which Method Should We Use?
Arc Length of the Curve y = f ( x )
Arc Length of the Curve x = g ( y )
Area of a Surface of Revolution
Mass and Density
Work Done by a Force
Work Done in Pumping
Hydrostatic Force and Pressure
Center of Mass and Moments
Center of Mass of Thin Plates
The Symmetry Principle
Theorem of Pappus
The Natural Logarithm as an Integral
Properties of the Natural Logarithm
Defining the Number e
The Exponential Function
Properties of the Exponential Function
General Logarithmic and Exponential Functions
Exponential Growth Model
Exponential Decay Model
Derivatives and Integrals of the Hyperbolic Functions
Calculus of Inverse Hyperbolic Functions
Applications