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Definite Integrals

Definite Integrals

Over or Under Estimates

Like the midpoint sum, whether the trapezoid sum gives an under- or over-estimate depends on the concavity of the function.

If our function is concave up, the trapezoids we get from the trapezoid rule cover too much area, so we get an overestimate.

If our function is concave down, the trapezoids don't cover enough area, so we get an underestimate.

If our function has no concavity (is a straight line), the trapezoid sum is just right. Which porridge will you pick, Goldilocks?

Whether the function is increasing or decreasing doesn't matter.

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