Name:
7.2b Notes on Trapezoidal Rule
Date:
Estimate the area under y  x 2  1 and above the x-axis between -1 and 3 using trapezoids. The
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general formula for the area of a trapezoid is A  h  b1  b2  .
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The Trapezoidal Rule
h
 y0  2 y1  2 y2  2 y3  ...  2 yn1  yn  ,
2
ba
where [a, b] is partitioned into n subintervals of equal length h 
.
n
To approximate the area under the curve, use T 
Now try the first problem using the formula!
Also, T 
LRAM n  RRAM n
. But be careful, the trapezoidal approximation is NOT the same as
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MRAM.
When a curve is concave up, the trapezoidal rule ________________the area under the curve.
When a curve is concave down, the trapezoidal rule __________________the area under the
curve.
Example 1: An observer measures the outside temperature every hour from noon until
midnight, recording the temperatures in the following table. What is the average temperature
for the 12-hour period? Use the trapezoidal rule.
Time N
Temp 63
1
65
2
66
3
68
4
70
5
69
6
68
7
68
8
65
9
64
10
62
Example 2: Find the area under the curve of 5x 4 on the interval [0, 2] with n = 1
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58
M
55