Math Problem Statement
Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the given curve about the y-axis. y = 9 - (x - 9)^2
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Volume of Solids
Cylindrical Shells Method
Formulas
V = 2π ∫(x * h(x)) dx
h(x) = 9 - (x - 9)^2
V = 2π ∫[6,12] x * (9 - (x - 9)^2) dx
Theorems
Cylindrical Shells Method
Definite Integral
Suitable Grade Level
College Calculus
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