CalculusVolume2-SASG-03-06
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
Chapter 3
Techniques of Integration
3.6 Numerical Integration
Section Exercises
Approximate the following integrals using either the midpoint rule, trapezoidal rule, or Simpson’s rule as indicated. (Round answers to three decimal places.)
299.
trapezoidal rule; Answer: 0.696
301.
trapezoidal rule; Answer: 9.298
303.
midpoint rule; Answer: 0.5000
305.
Use the trapezoidal rule with four subdivisions to estimate Answer: Approximate the integral to three decimal places using the indicated rule.
307.
trapezoidal rule; Answer: 0.500
309.
trapezoidal rule; Answer: 1.2819
311.
Simpson’s rule; Answer: 0.6577
313.
Simpson’s rule; Answer: 0.0213
OpenStax Calculus Volume 2
Student Answer and Solution Guide
315.
Simpson’s rule; Answer: 1.5629
317.
Approximate using the midpoint rule with four subdivisions to four decimal places. Answer: 1.9133
319.
Use the trapezoidal rule with four subdivisions to estimate to four decimal places.
Answer: 321.
Using Simpson’s rule with four subdivisions, find Answer: 1.0
323.
Given use the trapezoidal rule with 16 subdivisions to approximate the integral and find the absolute error. Answer: Approximate error is 0.000325.
325.
Find an upper bound for the error in estimating using the trapezoidal rule with seven subdivisions. Answer: 327.
Find an upper bound for the error in estimating using Simpson’s rule with
steps. Answer: 329.
Estimate the minimum number of subintervals needed to approximate the integral
with an error magnitude of less than 0.0001 using the trapezoidal rule.
OpenStax Calculus Volume 2
Student Answer and Solution Guide
Answer: 475
331.
Estimate the minimum number of subintervals needed to approximate the integral
with an error of magnitude less than 0.0001 using the trapezoidal rule. Answer: 174
333.
Use Simpson’s rule with four subdivisions to approximate the area under the probability density function from to Answer: 0.1544
335.
The length of one arch of the curve is given by Estimate L
using the trapezoidal rule with Answer: 6.2807
337.
Estimate the area of the surface generated by revolving the curve about the x
-axis. Use the trapezoidal rule with six subdivisions. Answer: 4.606
339.
The growth rate of a certain tree (in feet) is given by where t
is time in years. Estimate the growth of the tree through the end of the second year by using Simpson’s rule, using two subintervals. (Round the answer to the nearest hundredth.) Answer: 3.41 ft
341.
[T] Given approximate the value of this integral using the trapezoidal rule with 16 subdivisions and determine the absolute error. Answer: absolute error = 0.125
343.
The table represents the coordinates that give the boundary of a lot. The units of measurement are meters. Use the trapezoidal rule to estimate the number of square meters of land that is in this lot. X
y
x
y
0
125
600
95
100
125
700
88
200
120
800
75
300
112
900
35
400
90
1000
0
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
500
90
Answer: about 89,250 m
2
OpenStax Calculus Volume 2
Student Answer and Solution Guide
345.
The “Simpson” sum is based on the area under a ____. Answer: parabola
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