M120
Project 3
Date
due: 25 points [5 pt deduction for each class day late]
Objective: Area as a Riemann Sum, Trapezoid and
Simpson's Rule
1. For the integral 
, use the 'rectangle rule' to find an approximation to the
area
under the
curve.
a)
Use n
= 6 and the 'sum of rectangles' method three different times, according to
the value of 
. Show your work. These should be done using no program other
than EVALUATE or using the TABLE feature.
i) Use as the left
endpoint and find the sum
ii) Use as the right
endpoint and find the sum
iii) Finally use as the midpoint
of each interval and find the sum.
b)
Use your program to find the approximation using Trapezoid and Simpson's
with n
= 6.
2. For each of the following intervals, use the
'rectangle rule', with as the midpoint of the
interval. However, the value of n
should vary.
You may use a program on your calculator to find the sum of the midpoint
rectangles.
i) Each integral should be evaluated for n =
4, 10, 25, and 100.
ii)
Also each integral should be evaluated with Simpson's and Trapezoid for n = 100.
iii)
If indicated, the integral should also be evaluated using techniques
from chapters 6 & 7.
iv) Use the built-in numeric-integral on
your calculator also.
** See headings listed at the bottom
of this page.
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a) |
b) |
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c) |
d)
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You
might make a table for parts a) through d) with column headings:
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n = 4 |
n = 10 |
n = 25 |
n = 100 |
Trapezoid
Sum |
Simpson's
Sum |
Using
fnInt on Calculator |
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