GATE CE 2026 Set 2 — Question 13
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Engineering Mathematics → Partial Differential Equations → Fourier Series
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Question
Periodic function is given below.The CORRECT option representing the Fourier series expansion of is:
Correct answer
(A) f(x) = (4)/(π) [ sin x + (sin 3x)/(3) + (sin 5x)/(5) + … ]
Solution
The given function is an odd function because for the interval . For an odd function, the Fourier coefficients and are zero.
The coefficient is calculated as:
For even , . For odd , .
Substituting these into the Fourier series :
The coefficient is calculated as:
For even , . For odd , .
Substituting these into the Fourier series :
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