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)

5.1 Estimating Areas with Sums

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Example 2: Approximate the area enclosed between the graph of and the x-axis for 0 < x < 3 using MRAM and RRAM with 6 subintervals.

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Example 3: Approximate the distance traveled given the following data.

t (sec) v(t) (m/sec)0 010 5020 6530 7540 7550 6560 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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Trapezoidal RuleThe trapezoidal approximation using n trapezoids is

Simpson's Rule:

5.5 The Trapezoidal Rule and Simpson's Rule

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