Project ForgeEngineering Mathematics
Calculus
GATE 2022
Easy
The Fourier series expansion of x³ in the interval −1≤x<1 with periodic continuation has
- only sine terms
- Bonly cosine terms
- Cboth sine and cosine terms
- Donly sine terms and a non-zero constant
Explanation
x³ is an odd function (f(−x)=−f(x)). The Fourier series of any odd function, periodically continued on a symmetric interval, contains only sine terms — the cosine coefficients (including the constant a₀) vanish identically.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.