5.1 Estimating Areas with Sums
Rectangular Approximation Method (RAM)
LRAM (height of rectangle
is determined by the value
of the function at the
rectangle's LEFT edge)
RRAM (height of rectangle is
determined by the value of the
function at the rectangle's
RIGHT edge)
MRAM (height of rectangle is
determined by the value of the
function at the MIDPOINT of
the rectangle's base)
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Example 2: Approximate the area enclosed between the graph of
and the x-axis for 0 < x
with 6 subintervals.
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< 3 using MRAM and RRAM
Example 3: Approximate the distance
traveled given the following data.
t (sec) v(t) (m/sec)
0
0
10
50
30
75
50
65
20
40
60
65
75
60
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5.2 Definite Integrals
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5.3 Integrals as Antiderivatives
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Average Value of a Function
The average value of f(x) on [a,b] is
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5.4 The Fundamental Theorem of Calculus
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5.5 The Trapezoidal Rule and Simpson's Rule
Trapezoidal Rule
The trapezoidal approximation using n
trapezoids is
Simpson's Rule:
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