1. Trapezoidal Rule Questions on HW
Section 5.5
Trapezoidal Rule
Questions on HW

2. 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

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

4. Use the trapezoidal rule with n=4 to approximate
x0=a x1 x2 x3
x4=b

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

6. 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

7. 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

8. 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

9. Example 2: #58 p.319
Part c