Mr. Integral
Math notes/Calculus I/The Integral

Riemann Sums and Accumulation — Cheat sheet

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Core rule

Δx=(b−a)/n,\Delta x=(b-a)/n, ∫abf(x)dx=lim⁡n→∞∑i=1nf(xi∗)Δx.\int_a^bf(x)dx=\lim_{n\to\infty}\sum_{i=1}^nf(x_i^*)\Delta x.

Watch for

Include interval widths. Left/right bracketing requires monotonicity. Below-axis contributions are negative; total area integrates ∣f∣|f|.