Sketch and estimate the area of the region bounded by y = ln x, y = 0, x = 1, and x = 13 by using: a) 9 evenly spaced rectangles and right endpoints. Area estimate: 12.80182 (be sure to enter at least 5 correct decimal places!) Underestimate or Overestimate? Enter U or O: b) 7 evenly spaced rectangles and left endpoints. Area estimate: (be sure to enter at least 5 correct decimal places!) Underestimate or Overestimate? Enter U or O: c) 5 evenly spaced rectangles and midpoints. Area estimate: (be sure to enter at least 5 correct decimal places!) Underestimate or Overestimate? (It's harder to tell... take a guess!) Enter U or O:
Sketch and estimate the area of the region bounded by y = ln x, y = 0, x = 1, and x = 13 by using: a) 9 evenly spaced rectangles and right endpoints. Area estimate: 12.80182 (be sure to enter at least 5 correct decimal places!) Underestimate or Overestimate? Enter U or O: b) 7 evenly spaced rectangles and left endpoints. Area estimate: (be sure to enter at least 5 correct decimal places!) Underestimate or Overestimate? Enter U or O: c) 5 evenly spaced rectangles and midpoints. Area estimate: (be sure to enter at least 5 correct decimal places!) Underestimate or Overestimate? (It's harder to tell... take a guess!) Enter U or O:
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:Sketch and estimate the area of the region bounded by
y = ln x, y = 0, x = 1, and x
13 by using:
=
a) 9 evenly spaced rectangles and right endpoints.
Area estimate: 12.80182
(be sure to enter
at least 5 correct decimal places!)
Underestimate or Overestimate? Enter U or O:
b) 7 evenly spaced rectangles and left endpoints. Area
estimate:
(be sure to enter at
least 5 correct decimal places!)
Underestimate or Overestimate? Enter U or O:
c) 5 evenly spaced rectangles and midpoints. Area
estimate:
(be sure to enter at
least 5 correct decimal places!)
Underestimate or Overestimate? (It's harder to tell... take
a guess!) Enter U or O:
NOTE: To facilitate your calculations you may wish to
use the property of logarithms that
In x₁ + ln x₂ + + In x₂ = ln (x₁x2...Xn)
xn In
***
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