Study Guides

1.
Volumes by Slicing Help
Introduction to Volumes by Slicing When we learned the theory of the integral, we found that the basic idea was that one can calculate the area of an irregularly shaped region by subdividing the region into “rectangles.” We put the word ...
Source: McGrawHill Professional 
2.
Volumes of Solids of Revolution Help
Introduction to Volumes of Solids of Revolution A useful way—and one that we encounter frequently in everyday life—for generating solids is by revolving a planar region about an axis. For example, we can think of a ball (the interior of a sphere) as ...
Source: McGrawHill Professional 
3.
Principles of Work Help
Introduction to Principles of Work One of the basic principles of physics is that work performed is force times distance: If you apply force F pounds in moving an object d feet, then the work is
Source: McGrawHill Professional 
4.
Averages Help
Introduction to Averages In ordinary conversation, when we average a collection p 1,..., pk of k numbers, we add them together and divide by the number of items:
Source: McGrawHill Professional 
5.
Arc Length and Surface Area Help
Introduction Arc Length and Surface Area Just as the integral may be used to calculate planar area and spatial volume, so this tool may also be used to calculate the arc length of a curve and surface area. The basic idea is to approximate the length of a curve by ...
Source: McGrawHill Professional 
6.
Hydrostatic Pressure Help
Introduction to Hydrostatic Pressure If a liquid sits in a tank, then it exerts force on the side of the tank. This force is caused by gravity, and the greater the depth of the liquid then the greater the force. Pascal’s principle asserts that the ...
Source: McGrawHill Professional 
7.
The Trapezoid Rule Help
Introduction to The Trapezoid Rule While there are many integrals that we can calculate explicitly, there are many others that we cannot. For example, it is impossible to evaluate
Source: McGrawHill Professional 
8.
Applications of the Integral Practice Test
Review the following concepts if needed: Volumes by Slicing Help
Source: McGrawHill Professional 
9.
The Method of Cylindrical Shells Help
Introduction to The Method of Cylindrical Shells Our philosophy will now change. When we divide our region up into vertical strips, we will now rotate each strip about the y axis instead of the x axis. Thus, instead of generating a disk with ...
Source: McGrawHill Professional 
10.
Surface Area Help
Introduction to Surface Area Let f ( x ) be a nonnegative function on the interval [ a, b ]. Imagine rotating the graph of f about the x axis. This procedure will generate a surface of revolution, as shown in Fig. ...
Source: McGrawHill Professional

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