Math Problem Statement
. Find the Fourier series of period 2 for the function f(x) = x( 2 - x) in (0, 2 )
Solution
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Math Problem Analysis
Mathematical Concepts
Fourier Series
Integration
Odd and Even Functions
Trigonometric Functions
Formulas
Fourier series: f(x) = a_0/2 + Σ(a_n * cos(nx) + b_n * sin(nx))
Fourier coefficients: a_0 = (1/π)∫[0 to 2π] f(x) dx, a_n = (1/π)∫[0 to 2π] f(x) cos(nx) dx, b_n = (1/π)∫[0 to 2π] f(x) sin(nx) dx
Theorems
Fourier Series Expansion
Orthogonality of Sine and Cosine Functions
Suitable Grade Level
Undergraduate Mathematics