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Calculus: Applications of the Integral Help & Problems

Find study help on applications of the integral for calculus. Use the links below to select the specific area of applications of the integral you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn applications of the integral for calculus.

Study Guides

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  • 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 ...

  • 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 ...

  • 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

  • 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:

  • 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 ...

  • 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 ...

  • 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

  • 8.

    Applications of the Integral Practice Test

    Review the following concepts if needed: Volumes by Slicing Help

  • 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 ...

  • 10.

    Surface Area Help

    Introduction to Surface Area Let f ( x ) be a non-negative 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. ...

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