MathematicsGeneralQuality 61 · Exceptional

Integration as the Area Under a Curve

Donna Kelly Verified Teacher

@author · 2026-07-28 · v1

7 min read

Integration reverses differentiation and computes accumulated quantity.

\int_0^2 3x^2 \, dx = [x^3]_0^2 = 8

. Geometrically, this sums infinitesimal rectangles under

y = 3x^2

between 0 and 2, giving the total area — 8 square units.

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