Home · Unit 4 · Topic 1 · Applications of integration

Applications of integration

Use 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.

mm-u4-t1-s2-d3

Interactive

The trapezoidal rule

demo

Trapezoids on n equal panels approximate a definite integral over student-chosen [a, b]; compare the weighted sum to a reference value as n and the bounds change.

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