Calculus II (MATH222)
University Of Akron
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Calculus II- Chapter 6 Notes Bundle
- Voordeelbundel • 5 items • 2025
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This bundle includes class notes from the first major section of Calculus II. Topics include 6.1 Area Between Curves; 6.2 Disc and Washer Method; 6.3 Shell Method; 6.4 Work; and 6.5 Average Value of a Function; all dealing with basic integration techniques.
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6.5 Average Value of a Function
- College aantekeningen • 2 pagina's • 2025
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The average of some finite set of values is a familiar concept/computation. We generalize this idea to calculus where we are now asked to find the average value of a function using integration techniques. To do so, we fall back on the idea of approximation from Calc I.
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6.4 Work
- College aantekeningen • 5 pagina's • 2025
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We've been using integration since Calculus I, but several physical applications of the definite integral are common outside of math class, specifically in the departments of engineering and physics. In this section, we solve numerous problems dealing with work calculations in a variety of settings, with an emphasis on spring problems.
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6.3 Shell Method
- College aantekeningen • 4 pagina's • 2025
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Definite integrals can be used to find the volume of solids. In calculus, the "slicing method" of finding a solid's volume involves dividing that solid into many thin slices, estimating the volume of each slice, and then summing up those volumes through integration. In this section, we learn a method called the "shell method" that involves slicing a solid into smaller sections to find its overall volume. We also discuss the differences between the shell method, disc method, and wa...
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6.2 Disc and Washer Method
- College aantekeningen • 4 pagina's • 2025
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Definite integrals can be used to find the volume of solids. In calculus, the "slicing method" of finding a solid's volume involves dividing that solid into many thin slices, estimating the volume of each slice, and then summing up those volumes through integration. In this section, we learn two methods, namely the "disc method" and the "washer method," that involve slicing a solid into smaller sections to find its overall volume.
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6.1 Area Between Curves
- College aantekeningen • 4 pagina's • 2025
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Just as definite integrals can be used to find the area under a curve, they can also be used to find the area between two curves. In this section, we use a familiar concept from Calc I (that is, the Fundamental Theorem of Calculus) to determine the area enclosed by two or more curves after identifying points of intersection.
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