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**Trapezoidal Rule Questions on HW**

Section 5.5 Trapezoidal Rule Questions on HW

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**Approximate using LRAM w/ n=4**

Warm-Up Let Approximate using LRAM w/ n=4 Is LRAM an overestimate or underestimate? Approximate using RRAM w/ n=4 Is RRAM an overestimate or underestimate? Evaluate Solutions: LRAM – 23/4, underestimate RRAM – 31/4, overestimate Exact value - 20/3

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**Trapezoidal Rule Trapezoidal Rule: ( h = width of subinterval ) y(x)**

x0=a x1 x2 x3 x4=b Trapezoidal Rule: ( h = width of subinterval )

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**Use the trapezoidal rule with n=4 to approximate**

x0=a x1 x2 x3 x4=b

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**Use the trapezoidal rule with n=4 to approximate**

Example 1: Use the trapezoidal rule with n=4 to approximate

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Example 2: #58 p.319 The rate at which water flows out of a pipe is given by a differentiable function R of time t. The table below records the rate at 4-hour intervals for a 24-hour period. a) Use the Trapezoidal Rule with 6 subdivisions of equal length to approximate Explain the meaning of your answer in terms of water flow, using correct units. b) Is there some time t between 0 and 24 such that Justify your answer. c) Suppose the rate of water flow is approximated by Use Q(t) to approximate the average rate of water flow during the 24 hour period. t (hours) R(t) (gallons/hr) 9.6 4 10.3 8 10.9 12 11.1 16 20 10.5 24

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Example 2: #58 p.319 Part a This value approximates the total number of gallons of water that leaked out of the pipe from t=0 to t=24

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Example 2: #58 p.319 Part b Yes. Since R(t) is differentiable, it is also continuous. By the Mean Value Theorem, there is a number c between 0 and 24 such that

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Example 2: #58 p.319 Part c

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1 Example 1 (a) Estimate by the Midpoint, Trapezoid and Simpson's Rules using the regular partition P of the interval [0,2] into 6 subintervals. (b) Find.

1 Example 1 (a) Estimate by the Midpoint, Trapezoid and Simpson's Rules using the regular partition P of the interval [0,2] into 6 subintervals. (b) Find.

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