Integration applications include area, volume, work, and probability. Area under curve: A = ∫ₐᵇ f(x)dx (if f(x) ≥ 0). Area between curves: A = ∫ₐᵇ |f(x) - g(x)|dx. Volume of revolution (about x-axis): V = π∫ₐᵇ [f(x)]² dx. Work done: W = ∫ F(x)dx where F = force. Probability: For probability density function, P(a ≤ X ≤ b) = ∫ₐᵇ f(x)dx. Example: Area between y=x and y=x²: Intersection at 0,1. A = ∫₀¹ (x - x²)dx = [x²/2 - x³/3]₀¹ = 1/2 - 1/3 = 1/6. Exam tip: Set up integral correctly (limits, function order). Draw diagram. Include units.