Key Concepts: Integration in Area Calculations ⭐

Area Under a Curve

The area between a curve y = f(x) and the x-axis from x = a to x = b can be approximated using geometric methods.

Riemann Sums

• Divide the interval [a, b] into n equal subintervals of width Δx = (b − a)/n.
• Approximate area = sum of rectangle areas = Σ f(xᵢ) × Δx.
• As n → ∞, the approximation approaches the exact area.

Connection to Geometry

Area formulas for trapezoids and triangles are special cases of integration for linear functions. Circles and sectors relate to integration of curves.