∫₀^(π/2) cosx dx/(1 + sin²x) = কত?

ব্যাখ্যা

ধরি, sinx = z, cosx dx = dz; x = 0 হলে z = 0, x = π/2 হলে z = 1 ∴ ∫₀¹ dz/(1 + z²) = [tan⁻¹z]₀¹ = tan⁻¹(1) − tan⁻¹(0) = π/4