Evaluation of real integrals by contour integration
General · Mathematics
Study notes
Q: Evaluate ∫_{-∞}^∞dx/(x²+1). Close with semicircle (upper half-plane). Pole inside: z = i. Res: lim(z-i)/(z²+1) = 1/(2i). ∫ = 2πi×(1/2i) = π! Arc → 0 (ML: πR/R² → 0!). Answer: π (real integral via complex!).