In a half range sine series f(x)=e^x,0<x<1, the Fourier coefficient bn is given by
Question
Solution 1
The Fourier sine series for a function f(x) in the interval (0, L) is given by:
f(x) = Σ b_n * sin(nπx/L)
where the coefficients b_n are given by:
b_n = (2/L) * ∫_0^L f(x) * sin(nπx/L) dx
In this case, f(x) = e^x and L = 1, so we have:
b_n = 2 * ∫_0^1 e^x * sin(nπx) dx
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