Fundamental theorem of calculus and definite integrals
Mathematical Methods · Unit 4 — Further calculus, trigonometry and statistics · Further integration
Learning objectives (3)
LO-1Understand the fundamental theorem of calculus, ∫ 𝑓(𝑥) 𝑏 𝑎 𝑑𝑥 = 𝐹(𝑏) − 𝐹(𝑎), and use it to calculate definite integrals.LO-2Use sums of the form ∑ 𝑓(𝑥𝑖) 𝛿𝑥𝑖𝑖 to estimate the area under the curve 𝑦 = 𝑓(𝑥).LO-3Use the definite integral ∫ 𝑓(𝑥) 𝑏 𝑎 𝑑𝑥 to determine the area under the curve 𝑦 = 𝑓(𝑥) between 𝑥 = 𝑎 and 𝑥 = 𝑏 if 𝑓(𝑥) > 0 over this interval.
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