Revolution
Definition
In calculus, revolution refers to rotating a curve or shape around an axis. This rotation allows us to calculate various properties such as surface area and volume using techniques like disk and washer methods.
Analogy
Imagine a dancer spinning around on one leg. The revolution of the dancer represents the rotation of a curve or shape, allowing us to analyze its properties using calculus techniques.
Related terms
Disk Method: A technique that uses revolution to find volumes by integrating cross-sectional areas of infinitesimally thin disks.
Washer Method: Another technique that uses revolution to find volumes by subtracting inner volumes from outer volumes using concentric circles.
Surface area: The total area covering the curved surface of a solid, which can be calculated using revolution and other calculus techniques.
"Revolution" appears in:
Subjects (6)
Study guides (1)
Practice Questions (2)
Consider a region defined by the function g(y) = √(4-y^2), revolved around the y-axis from y = 0 to y = 2. What is the volume of the solid formed by this revolution?
Consider a region defined by the function f(x) = x^2, revolved around the x-axis from x = 0 to x = 1. What is the volume of the solid formed by this revolution?
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