(a) Use six rectangles to find estimates of each type for the area under the given graph of f, the x-axis, and the lines x = 0 and x = 12. (i) L (sample points are left endpoints) 46 = (ii) R (sample points are right endpoints) R6 = (iii) M (sample points are midpoints) M6 (b) Is L an underestimate or overestimate of the true area? overestimate underestimate (c) Is R an underestimate or overestimate of the true area? overestimate underestimate OO

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The graph of the function f is given.
y
y = f(x)
4
2
X
0
2
4 6 8 10 12
(a) Use six rectangles to find estimates of each type for the area under the given graph of f, the x-axis, and the lines x = 0 and x = 12.
(i) L (sample points are left endpoints)
=
46
(ii) R (sample points are right endpoints)
R6
=
(iii) M6 (sample points are midpoints)
M6
=
(b) Is L an underestimate or overestimate of the true area?
6
overestimate
underestimate
(c) Is R6 an underestimate or overestimate of the true area?
overestimate
underestimate
(d) Which of the numbers!
D or M
O O
8
6
OO
gives the best estimate of the true area?
Transcribed Image Text:The graph of the function f is given. y y = f(x) 4 2 X 0 2 4 6 8 10 12 (a) Use six rectangles to find estimates of each type for the area under the given graph of f, the x-axis, and the lines x = 0 and x = 12. (i) L (sample points are left endpoints) = 46 (ii) R (sample points are right endpoints) R6 = (iii) M6 (sample points are midpoints) M6 = (b) Is L an underestimate or overestimate of the true area? 6 overestimate underestimate (c) Is R6 an underestimate or overestimate of the true area? overestimate underestimate (d) Which of the numbers! D or M O O 8 6 OO gives the best estimate of the true area?
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