The Definite Integral

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The Definite Integral

• The old train problem
• A train moves along a track at a steady rate of
  80 miles per hour from 800 a.m. until 1000 a.m.
  What is the total distance traveled by the
  train?

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Jenna What happens when
the region is curved?
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Maci When the region is curved, you could
divide it into shapes to fill the region and then
find the area of each of the shapes.
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RRAM
RECTANGULAR APPROXIMATION METHOD
LRAM
MRAM
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TRAPEZOID RULE

• Another geometric shape to
• approximate the area under
• the curve is the trapezoid.

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TRAPEZOID RULE
where a, b is partitioned into n subintervals
of equal length
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TRAPEZOID RULE
Equivalently
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Estimate the area under the following curve using
LRAM, MRAM, RRAM and the TRAPEZOID RULE
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LRAM
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RRAM
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MRAM
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The Trapezoid Rule
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Calculus
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