Home · Unit 4 · Topic 1 · Fundamental theorem of calculus and definite integrals

Fundamental theorem of calculus and definite integrals

Use sums of the form ∑ 𝑓(𝑥𝑖) 𝛿𝑥𝑖𝑖 to estimate the area under the curve 𝑦 = 𝑓(𝑥).

mm-u4-t1-s1-d1

Interactive

Rectangle sums → the definite integral

manipulative

Left, midpoint, or right rectangles estimate area under y = f(x); scrub n, endpoints, and shape params — compare the sum to the definite integral as n grows.

Open fullscreen →

Want a different take?

Already have one and want another angle on this point? Describe what students should notice. Requests are read and acted on.