Practice question · True or false
A Riemann sum with more rectangles is always a better approximation than one with fewer.
Hints
- Compare a fine left sum with a coarse midpoint sum.
- The rule matters as well as the count.
Show the answer
False
Why
False. The rule matters too: a midpoint or trapezoid sum with four intervals routinely beats a left-endpoint sum with forty, because the endpoint rules have first-order error while the midpoint rule's cancels to second order. More rectangles help within a rule, not across rules.
Practise The Definite Integral
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