Integration: area & kinematics

∫axⁿ = axⁿ⁺¹/(n+1) + c; definite = top − bottom. Exam-style Area under y = 4x − x², x = 0…4 Evaluate. ∫₀⁴ (4x − x²)dx = [2x² − x³/3]₀⁴ = (32 − 64/3) − 0 = 32/3 ✓ ≈ 10.7 units². Curve stays above the axis, so the integral is the area.

Kinematics

Differentiate down the chain: s → v → a.
Integrate up: a → v → s, using initial conditions for +c.
Rest: v = 0. Distance travelled = area under v–t.

Practice for this standard covers the whole topic — flashcards and quiz.