Applications of integration

Mathematical Methods · Unit 4 — Further calculus, trigonometry and statistics · Further integration

Learning objectives (5)

LO-1Calculate the area between curves, with and without technology.LO-2Calculate the area enclosed by a curve and the 𝑥-axis over a given domain, with and without technology.LO-3Calculate total change by integrating instantaneous or marginal rates of change, with and without technology.LO-4Model and solve problems that involve definite integrals, including motion problems, with and without technology.LO-5Use the trapezoidal rule, ∫ 𝑓(𝑥) 𝑏 𝑎 𝑑𝑥 ≈ 𝑤 2 [𝑓(𝑥0) + 2(𝑓(𝑥1) + 𝑓(𝑥2) + 𝑓(𝑥3)+... 𝑓(𝑥𝑛−1)) + 𝑓(𝑥𝑛)], where 𝑤 = 𝑏−𝑎 𝑛, to approximate an area and the value of a definite integral, with and without technology.

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