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(Homework)
SMALL BRIAN DIXON
MA 241, section 009, Fall
2005
Instructor: Drew Pasteur
North Carolina State
University
About this Assignment
Due: Thursday, September 8, 2005 11:12 PM EDT
Current Score: 14.25 out of 14.25
Question Score
Description
Approximate
Integration
pts subs
1 0.25/0.25 4/20
2 0.25/0.25 2/20
3 0.25/0.25 3/20
4 0.25/0.25 1/20
5 0.5/0.5 3/20
6 0.5/0.5 2/20
2/2
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Notes
1.
[SCalcCC2 5.9.02.]
The left, right, Trapezoidal, and Midpoint Rule
approximations were used to estimate the following where f is the
function whose graph is shown below it.
The estimates were 0.7816 , 0.8676 , 0.8631 , and 0.9530 , and the
same number of subintervals were used in each case.
(a) Which rule produced which estimate?
L
n
= 0.9530 [ 0.9530 ]
T
n
= 0.8676 [ 0.8676 ]
M
n
= 0.8631 [ 0.8631 ]
R
n
= 0.7816 [ 0.7816 ]
(b) Between which two approximations does the true
value of the integral lie?
0.8631 [ 0.8631 ] (smaller approximation)
0.8676 [ 0.8676 ] (larger approximation)

pts subs
1 0.25/0.25 1/20
2 0.25/0.25 2/20
3 0.25/0.25 1/20
4 0.25/0.25 2/20
5 .2/.2 1/20
6 .2/.2 3/20
7 .2/.2 5/20
8 .2/.2 4/20
9 .2/.2 2/20
10 0.5/0.5 1/20
11 0.5/0.5 1/20
12 0.5/0.5 1/20
13 0.5/0.5 1/20
14 0.25/0.25 3/20
4.25/4.25