The rectangles in the graph below illustrate a left endpoint upper sum for f(x) = 17 on the interval (2, 6). The value of this left endpoint upper sum is and this upper sum is an ? + the area of the region enclosed by y = f(x), the x- axis, and the vertical lines x = 2 and x = 6. 8. 4. 2 6 8 Left endpoint upper sum for y = 17 on [2, 6] The rectangles in the graph below illustrate a right endpoint lower sum for f(æ) = 17 on the interval [2, 6]. The value of this right endpoint lower sum is and this lower sum is an ? + the area of the region enclosed by y = f(x), the x- axis, and the vertical lines x = 2 and x = 6.
The rectangles in the graph below illustrate a left endpoint upper sum for f(x) = 17 on the interval (2, 6). The value of this left endpoint upper sum is and this upper sum is an ? + the area of the region enclosed by y = f(x), the x- axis, and the vertical lines x = 2 and x = 6. 8. 4. 2 6 8 Left endpoint upper sum for y = 17 on [2, 6] The rectangles in the graph below illustrate a right endpoint lower sum for f(æ) = 17 on the interval [2, 6]. The value of this right endpoint lower sum is and this lower sum is an ? + the area of the region enclosed by y = f(x), the x- axis, and the vertical lines x = 2 and x = 6.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The rectangles in the graph below illustrate a left endpoint upper sum for f(x) =
17
on the interval 2, 6).
The value of this left endpoint upper sum is
and this upper sum is an ?
A the area of the region enclosed by y = f(x), the x-
axis, and the vertical lines x = 2 and x = 6.
8
7
6
2
1
2
6
7
8
Left endpoint upper sum for y = 17 on [2, 6]
The rectangles in the graph below illustrate a right endpoint lower sum for f(x) =
17
on the interval (2, 6].
The value of this right endpoint lower sum is
and this lower sum is an ?
+ the area of the region enclosed by y = f(æ), the x-
axis, and the vertical lines x = 2 and x = 6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8c59ec9-a5d7-4863-9fb4-b71ac17a51c9%2Facc638aa-a619-4204-a1ce-37ae5d35c2d8%2Fzdsrwif_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The rectangles in the graph below illustrate a left endpoint upper sum for f(x) =
17
on the interval 2, 6).
The value of this left endpoint upper sum is
and this upper sum is an ?
A the area of the region enclosed by y = f(x), the x-
axis, and the vertical lines x = 2 and x = 6.
8
7
6
2
1
2
6
7
8
Left endpoint upper sum for y = 17 on [2, 6]
The rectangles in the graph below illustrate a right endpoint lower sum for f(x) =
17
on the interval (2, 6].
The value of this right endpoint lower sum is
and this lower sum is an ?
+ the area of the region enclosed by y = f(æ), the x-
axis, and the vertical lines x = 2 and x = 6.
![1
1
2 3
4
5
6
8
Left endpoint upper sum for y =
17
on [2, 6]
The rectangles in the graph below illustrate a right endpoint lower sum for f(x)
17
on the interval [2, 6].
The value of this right endpoint lower sum is
and this lower sum is an ?
+ the area of the region enclosed by y = f(x), the x-
axis, and the vertical lines x = 2 and x = 6.
8
1
3
4
8.
Right endpoint lower sum fory
17 on 2, 6]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8c59ec9-a5d7-4863-9fb4-b71ac17a51c9%2Facc638aa-a619-4204-a1ce-37ae5d35c2d8%2Fnvcl0mb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1
1
2 3
4
5
6
8
Left endpoint upper sum for y =
17
on [2, 6]
The rectangles in the graph below illustrate a right endpoint lower sum for f(x)
17
on the interval [2, 6].
The value of this right endpoint lower sum is
and this lower sum is an ?
+ the area of the region enclosed by y = f(x), the x-
axis, and the vertical lines x = 2 and x = 6.
8
1
3
4
8.
Right endpoint lower sum fory
17 on 2, 6]
Expert Solution
Step 1
We can find the value of the integral using left end point or right end point by taking the sum of the areas of the rectangles made in the interval taking height equal to the value at left end point or at right endpoint respectively. Also for a decreasing curve the value found in left end point method is an overestimate of the area where as in right end point method the value found is an underestimate of the area.
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