Math Problem Statement

Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the x-axis. y =

81 − x2 , −8 ≤ x ≤ 8

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Surface Area of Revolution
Definite Integrals
Symmetry in Curves

Formulas

Surface area of revolution around the x-axis: A = 2π ∫[a, b] y √(1 + (dy/dx)^2) dx
Derivative of y = 81 - x^2: dy/dx = -2x

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12, College Level