Let fx) = 4 + x. (a) Estimate the ares under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints. R, Improve your estimate by using six rectangles. Sch the oune and he aporoumating rectangies for O o- O o- Sth the unve and the onating ectongies tor 13 o- -as 03 I 13 o- 13 0 o-1 13 O o-1 13 epet pet nganpores ne n enes 0-1 10-1
Let fx) = 4 + x. (a) Estimate the ares under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints. R, Improve your estimate by using six rectangles. Sch the oune and he aporoumating rectangies for O o- O o- Sth the unve and the onating ectongies tor 13 o- -as 03 I 13 o- 13 0 o-1 13 O o-1 13 epet pet nganpores ne n enes 0-1 10-1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let fx) = 4 + 4x.
Sketch the curve and the approximating rectangles for
(a) Estimate the area under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints.
20
2아
20
R =
15
15
15
13
Improve your estimate by using six rectangles.
10
10
10
Sketch the curve and the approximating rectangies for R
2아
20
o-1
2"O o-1
-0.5
2 0 0-1 -0.5
2 0 0-1
-0.5
0.5
0.5
15
0.5 1
15
-05
0.5
1.5
13
13
13
15
(c) Repeat part (a) using a midpoints
10
M. -0
Sketch the curve and the approximating rectangles for M
20
15
15
15
15
o-1
O 0-1
0 0-1
O 0-1
Sketch the curve and the approximating rectangles for R
o-1
O -1
O o-1
O o-1
2아
20-
2아
Sketch the curve and the approximating rectangles for M
15
13
15
15
2아
10
10
1아
10
15
13
13
15
10
10
10
10
0 0-1
0.5
O 0-1
1
o-1
-0.5
0.5
15
-0.5
0.5
15
0 0-1
-0.5
-0.5
0.5
15
(b) Repeat part (a) using a left enapoints.
o-1
O 0-1
O o-1
0.5 1
O o-1
-a.5
0.5
1.5
-05
1
15
-a.5
1.5
-a.s
0.5
1.5
Sketch the curve and the approximating rectangies for
(4) From your skatches in parts (a)-(c), which estimate appears to be the most accurate?
2아
OR
15
15-
13
10
O 0-1
0 0-1
0-1
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