Riemann integration
General · Mathematics
Study notes
Q: Show f(x) = x² is integrable on [0,1] and compute ∫₀¹x²dx via FTC. Continuous → integrable ✓. Antiderivative: x³/3. FTC: 1/3 - 0 = 1/3. (Riemann sums: (1/n³)Σk² → 1/3 - matches!) Dirichlet (1 on ℚ): NOT Riemann integrable (U-L = 1 always)!