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 Homework Statement:
 Find the Fourier Coefficient
 Relevant Equations:

##f:[0,1]\rightarrow \mathbb{R}## given by
$$f(x)=x^2$$
Consider the function ##f:[0,1]\rightarrow \mathbb{R}## given by
$$f(x)=x^2$$
(1) The Fourier coefficients of ##f## are given by
$$\hat{f}(0)=\int^1_0x^2dx=\Big[\frac{x^3}{3}\Big]^1_0=\frac{1}{3}$$
$$\hat{f}(k)=\int^1_0x^2e^{2\pi i k x}dx$$
Can this second integral be evaluated?
$$f(x)=x^2$$
(1) The Fourier coefficients of ##f## are given by
$$\hat{f}(0)=\int^1_0x^2dx=\Big[\frac{x^3}{3}\Big]^1_0=\frac{1}{3}$$
$$\hat{f}(k)=\int^1_0x^2e^{2\pi i k x}dx$$
Can this second integral be evaluated?