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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?