How do you determine the volume of a solid created

Micaela Simon 2022-06-30 Answered
How do you determine the volume of a solid created by revolving a function around an axis?
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Answers (1)

Belen Bentley
Answered 2022-07-01 Author has 28 answers
Given a function f(x) and an interval [a,b] we can think of the solid formed by revolving the graph of f(x) around the x axis as a horizontal stack of an infinite number of infinitesimally thin disks, each of radius f(x).
The area of a circle is π r 2 , so the area of the circle at a point x will be π f ( x ) 2
The volume of the solid is then the infinite sum of the infinitesimally thin disks over the interval [a,b]
So:
Volume = a b π f ( x ) 2 d x = π a b f ( x ) 2 d x
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