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Unit: Accumulation and Riemann sums

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Definite integrals intro

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Finding definite integrals using area formulasGet 3 of 4 questions to level up!
Definite integral by thinking about the function's graphGet 3 of 4 questions to level up!

Left & right Riemann sums

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Left & right Riemann sumsGet 3 of 4 questions to level up!
Over- and under-estimation of Riemann sumsGet 3 of 4 questions to level up!

Midpoint & trapezoidal sums

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Midpoint & trapezoidal sumsGet 3 of 4 questions to level up!

Quiz 1

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Summation notation

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Summation notation introGet 3 of 4 questions to level up!
Summation notationGet 3 of 4 questions to level up!

Riemann sums in summation notation

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Riemann sums in summation notationGet 3 of 4 questions to level up!

Definite integral as the limit of a Riemann sum

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Definite integral as the limit of a Riemann sumGet 3 of 4 questions to level up!

Quiz 2

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Definite integrals properties

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Using multiple properties of definite integralsGet 3 of 4 questions to level up!
Definite integrals over adjacent intervalsGet 3 of 4 questions to level up!
Finding definite integrals using algebraic propertiesGet 3 of 4 questions to level up!

Functions defined by integrals

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Functions defined by definite integrals (accumulation functions)Get 3 of 4 questions to level up!

Quiz 3

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Unit test

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About this unit

The definite integral represents the area under the graph of a function between two vertical lines. Sometimes this area isn't found so easily, but we can always estimate it using simpler shapes like rectangles. In fact, the formal definition of the definite integral is based on these approximations, which are called Riemann sums.