GATE XE (Engineering Sciences) 2024 - Question 11

Section: Engineering Mathematics | Marks: 1

Let 𝑓(𝑥) = {𝜋+ 𝑥,⁡⁡⁡⁡⁡⁡⁡ −𝜋≤𝑥< 0, ⁡⁡⁡0,⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡0 ≤𝑥< 𝜋, with 𝑓(𝑥+ 2𝜋) = 𝑓(𝑥). If 𝐹(𝑥) represents the Fourier series of 𝑓(𝑥), then the value of 𝐹(− 𝜋 2) + 𝐹(0) is

• A. 0
• B. 𝜋 2
• C. 𝜋
• D. 3𝜋 2

Answer: C. 𝜋