Applications of integration

OpenStax

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Areas between curves

Determining volumes by slicing

1 Volume and the slicing method

2 Solids of revolution

3 The disk method

4 The washer method

6 Key equations

Volumes of revolution: cylindrical shells

1 The method of cylindrical shells

2 Which method should we use?

4 Key equations

Arc length of a curve and surface area

1 Arc length of the curve y = f ( x )

2 Arc length of the curve x = g ( y )

3 Area of a surface of revolution

5 Key equations

Physical applications

Moments and centers of mass

1 Center of mass and moments

2 Center of mass of thin plates

3 The symmetry principle

4 Theorem of pappus

7 Key equations

Integrals, exponential functions, and logarithms

1 The natural logarithm as an integral

2 Properties of the natural logarithm

4 Defining the number e

5 The exponential function

6 Properties of the exponential function

8 General logarithmic and exponential functions

10 Key equations

Exponential growth and decay

1 Exponential growth model

2 Exponential decay model

Calculus of the hyperbolic functions

Source: OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2

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