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General Information
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For Students
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For Instructors
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Miscellaneous
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Applications of Integration
- Area Between Curves
- Applet 1 (Graph and Calculation of the Area between two curves)
- Working Example 1 (Area Between 2 Curves with Visualization) : Integrals are used to find the area between two curves. An integral formula is developed and its applicability is discussed in a variety of examples.
- Applet 2 (Area Between two Curves)
- Arc Length
- Working Example 2 (Visualization of the Arclength Integral)
- Applet 3 (Numerical Approximation + Visualization) : Another illustration of the Riemann Sum modeling method is given, this time to compute the length of a curve in the plane. An integral formula is developed to compute the arc length. It is pointed out that the formula often leads to integrals that must be approximated by numerical methods.
- Applet 4 (Arc Length)
- Volumes of Solids of Revolution
- Applet 5 (A Riemann Sum for a Solid of Revolution) : Integrals find application in many modeling situations involving continuous variables such as area. They allow us to model physical entities that can be described through a process of adding up, or accumulating, smaller infinitesimal parts. In this section, the Riemann Sum approach is used to develop an integral formula for the volume of a solid of revolution.
- Surfaces of Revolution
- Numerical Approximations
- Applet 7 (Trapezoid Rule Visualization) : Many applications of calculus involve definite integrals. If it is possible to find an antiderivative for the integrand, then the integral can be evaluated using the Fundamental Theorem. When an antiderivative is not apparent, numerical (approximate) methods are invoked. The numerical method that is discussed in this section is called the Trapezoid Rule.
- Work
- Expected Value
Look at all MATH online learning modules.
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