Anti-differentiation
Mathematical Methods · Unit 3 — Further calculus and introduction to statistics · Introduction to integration
Learning objectives (11)
LO-1Determine displacement given acceleration and initial values of displacement and vel ocity.LO-2Determine displacement given velocity and the initial value of displacement.LO-3Determine 𝑓(𝑥) given 𝑓′(𝑥) and an initial condition 𝑓(𝑎) = 𝑏.LO-4Determine indefinite integrals of the form ∫ 𝑓(𝑎𝑥 + 𝑏)𝑑𝑥.LO-5Model and solve problems that involve indefinite integrals, with and without technology. Mathematical Methods 2025 v1.3LO-6Understand and use the formulas ∫(𝑓(𝑥) + 𝑔(𝑥))𝑑𝑥 = ∫ 𝑓(𝑥)𝑑𝑥 + ∫ 𝑔(𝑥) 𝑑𝑥 and ∫ 𝑘 𝑓(𝑥)𝑑𝑥 = 𝑘 ∫ 𝑓(𝑥)𝑑𝑥.LO-7Use the formula ∫ 1 𝑥 𝑑𝑥 = ln(𝑥) + 𝑐, for 𝑥 > 0.LO-8Use the formula ∫ 𝑒𝑥 𝑑𝑥 = 𝑒𝑥 + 𝑐.LO-9Use the formula ∫ 𝑥𝑛 𝑑𝑥 = 𝑥𝑛+1 𝑛+1 + 𝑐 for 𝑛 ≠ − 1.LO-10Use the formulas ∫ sin (𝑥) 𝑑𝑥 = − cos(𝑥) + 𝑐 and ∫ cos(𝑥) 𝑑𝑥 = sin (𝑥) + 𝑐.LO-11Use the notation ∫ 𝑓(𝑥) 𝑑𝑥 for anti-derivatives or indefinite integrals.
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