12 Suppose f(x) X (a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for f(x) on the interval 3 ≤ x ≤ 5. The value of this left endpoint Riemann sum is , and it is an ? the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and x = 5. (b) The rectangles in the graph on the right illustrate a right endpoint Riemann sum for f(x) on the interval 3 ≤ x ≤ 5. The value of this right endpoint Riemann sum is and it is an? the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and x = 5. 8 7 6 5 4 3 2 1 Y 1 2 3 4 5 6 7 8 Left endpoint Riemann sum 8 7 6 5 4 3 2 1 y 1 2 3 4 5 6 7 8 Right endpoint Riemann sum
12 Suppose f(x) X (a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for f(x) on the interval 3 ≤ x ≤ 5. The value of this left endpoint Riemann sum is , and it is an ? the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and x = 5. (b) The rectangles in the graph on the right illustrate a right endpoint Riemann sum for f(x) on the interval 3 ≤ x ≤ 5. The value of this right endpoint Riemann sum is and it is an? the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and x = 5. 8 7 6 5 4 3 2 1 Y 1 2 3 4 5 6 7 8 Left endpoint Riemann sum 8 7 6 5 4 3 2 1 y 1 2 3 4 5 6 7 8 Right endpoint Riemann sum
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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Question
![**Suppose \( f(x) = \frac{12}{x} \).**
(a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for \( f(x) \) on the interval \( 3 \leq x \leq 5 \). The value of this left endpoint Riemann sum is [input box], and it is an [dropdown box] the area of the region enclosed by \( y = f(x) \), the x-axis, and the vertical lines \( x = 3 \) and \( x = 5 \).
(b) The rectangles in the graph on the right illustrate a right endpoint Riemann sum for \( f(x) \) on the interval \( 3 \leq x \leq 5 \). The value of this right endpoint Riemann sum is [input box], and it is an [dropdown box] the area of the region enclosed by \( y = f(x) \), the x-axis, and the vertical lines \( x = 3 \) and \( x = 5 \).
**Graphs:**
- **Left Endpoint Riemann Sum:** The graph on the left shows rectangles under the curve of \( y = f(x) \). The height of each rectangle is determined by the function value at the left endpoint of each subinterval between \( x = 3 \) and \( x = 5 \).
- **Right Endpoint Riemann Sum:** Conversely, the graph on the right uses the function value at the right endpoint of each subinterval to determine the height of the rectangles, forming a different approximation for the same interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7154a3f3-e619-45a8-a06e-684279d32bee%2F53f3c8da-5296-4dbe-8823-387dc5c78ced%2F8tj8hgj_processed.png&w=3840&q=75)
Transcribed Image Text:**Suppose \( f(x) = \frac{12}{x} \).**
(a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for \( f(x) \) on the interval \( 3 \leq x \leq 5 \). The value of this left endpoint Riemann sum is [input box], and it is an [dropdown box] the area of the region enclosed by \( y = f(x) \), the x-axis, and the vertical lines \( x = 3 \) and \( x = 5 \).
(b) The rectangles in the graph on the right illustrate a right endpoint Riemann sum for \( f(x) \) on the interval \( 3 \leq x \leq 5 \). The value of this right endpoint Riemann sum is [input box], and it is an [dropdown box] the area of the region enclosed by \( y = f(x) \), the x-axis, and the vertical lines \( x = 3 \) and \( x = 5 \).
**Graphs:**
- **Left Endpoint Riemann Sum:** The graph on the left shows rectangles under the curve of \( y = f(x) \). The height of each rectangle is determined by the function value at the left endpoint of each subinterval between \( x = 3 \) and \( x = 5 \).
- **Right Endpoint Riemann Sum:** Conversely, the graph on the right uses the function value at the right endpoint of each subinterval to determine the height of the rectangles, forming a different approximation for the same interval.
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