Suppose f(x) 8 (a) The rectangles in the graph on the left illustrate a left endpoint upper sum for f(x) on the interval 3 < x < 5. and it is an underestimate of 4 the area of the region The value of this left endpoint upper sum is Right endpoint enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and x = 5. Left endpoint upper sum (b) The rectangles in the graph on the right illustrate a right endpoint lower sum for f(x) on the interval 3 < x < 5 . The value of this right endpoint lower sum is lower sum and it is an overestimate of the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and r = 5.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose
x²
f(x) =
8
(a) The rectangles in the graph on the left illustrate a left endpoint upper sum for f(x) on the interval 3 < x < 5.
The value of this left endpoint upper sum is
and it is an underestimate of + the area of the region
1234SSTI
Right
endpoint
enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and x = 5.
Left endpoint
upper sum
(b) The rectangles in the graph on the right illustrate a right endpoint lower sum for f(x) on the interval 3 < x < 5
. The value of this right endpoint lower sum is
lower sum
and it is an overestimate of
the area of the region
enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and a = 5.
Transcribed Image Text:Suppose x² f(x) = 8 (a) The rectangles in the graph on the left illustrate a left endpoint upper sum for f(x) on the interval 3 < x < 5. The value of this left endpoint upper sum is and it is an underestimate of + the area of the region 1234SSTI Right endpoint enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and x = 5. Left endpoint upper sum (b) The rectangles in the graph on the right illustrate a right endpoint lower sum for f(x) on the interval 3 < x < 5 . The value of this right endpoint lower sum is lower sum and it is an overestimate of the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and a = 5.
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