Ngô Quốc Anh

July 17, 2009

3 indefinite integral problems involving sinx/x via residue


Problem 1. Compute

\displaystyle\int\limits_{ - \infty }^\infty {\frac{{\sin x}} {x}dx}

via complex variable methods.

Problem 2. Compute

\displaystyle\int\limits_{ - \infty }^\infty {\frac{{\sin^2 x}} {x^2}dx}

via complex variable methods.

Problem 3. Compute

\displaystyle\int\limits_{ - \infty }^\infty {\frac{{\sin^3 x}} {x^3}dx}

via complex variable methods.

(more…)

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