The rectangles in the graph below illustrate a right endpoint Riemann sum for f(x) = (15/x) on the interval [3, 7]. The value of this right endpoint Riemann sum is and this Riemann sum is [select an answer] the area of the region enclosed by y = f(æ), the x-axis, and the vertical lines x = 3 and %3D x = 7. y 8 4 3
The rectangles in the graph below illustrate a right endpoint Riemann sum for f(x) = (15/x) on the interval [3, 7]. The value of this right endpoint Riemann sum is and this Riemann sum is [select an answer] the area of the region enclosed by y = f(æ), the x-axis, and the vertical lines x = 3 and %3D x = 7. y 8 4 3
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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![The image illustrates a graph representing the function \( y = \frac{15}{x} \) on the interval \([3, 7]\). The graph features a blue curve representing the function. Under the curve, there are several blue rectangular bars, which form a right endpoint Riemann sum approximation of the area under the curve from \( x = 3 \) to \( x = 7 \).
### Explanation of the Graph:
- **Axes**:
- The horizontal axis is labeled as \( x \), ranging from 0 to 8.
- The vertical axis is labeled as \( y \), ranging from 0 to 8.
- **Curve**:
- The curve shows the function \( y = \frac{15}{x} \). The curve is decreasing as \( x \) increases.
- **Riemann Sum**:
- The rectangles' heights are determined by the function value at the right endpoint of subintervals on \( [3, 7] \).
- These rectangles provide an approximation of the integral of the function, representing the total area under the curve over the specified interval.
This visualization demonstrates the method of approximating definite integrals using right endpoint Riemann sums, which is an important concept in calculus for estimating the area under a curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F601ccad1-4d17-4947-9a80-69495cb62ebb%2F3c1a5f19-dab2-49f8-9d5e-e59f74f837ce%2Faeqrhmu_processed.png&w=3840&q=75)
Transcribed Image Text:The image illustrates a graph representing the function \( y = \frac{15}{x} \) on the interval \([3, 7]\). The graph features a blue curve representing the function. Under the curve, there are several blue rectangular bars, which form a right endpoint Riemann sum approximation of the area under the curve from \( x = 3 \) to \( x = 7 \).
### Explanation of the Graph:
- **Axes**:
- The horizontal axis is labeled as \( x \), ranging from 0 to 8.
- The vertical axis is labeled as \( y \), ranging from 0 to 8.
- **Curve**:
- The curve shows the function \( y = \frac{15}{x} \). The curve is decreasing as \( x \) increases.
- **Riemann Sum**:
- The rectangles' heights are determined by the function value at the right endpoint of subintervals on \( [3, 7] \).
- These rectangles provide an approximation of the integral of the function, representing the total area under the curve over the specified interval.
This visualization demonstrates the method of approximating definite integrals using right endpoint Riemann sums, which is an important concept in calculus for estimating the area under a curve.
![The rectangles in the graph below illustrate a right endpoint Riemann sum for \( f(x) = \frac{15}{x} \) on the interval \([3, 7]\).
The value of this right endpoint Riemann sum is \(\_\_\_\_\_\_\_\_\_\_\_\), and this Riemann sum is \([ \text{select an answer} ]\) the area of the region enclosed by \( y = f(x) \), the x-axis, and the vertical lines \( x = 3 \) and \( x = 7 \).
**Graph Explanation:**
The graph displays the function \( f(x) = \frac{15}{x} \) with a curve descending from left to right. Blue rectangles are used to approximate the area under the curve from \( x = 3 \) to \( x = 7 \). These rectangles represent the right endpoint Riemann sum, where the height of each rectangle is determined by the function value at the right endpoint of each subinterval. The x-axis is labeled from 3 to 7, and the y-axis has values labeled from 0 to 9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F601ccad1-4d17-4947-9a80-69495cb62ebb%2F3c1a5f19-dab2-49f8-9d5e-e59f74f837ce%2F9kx0kzi_processed.png&w=3840&q=75)
Transcribed Image Text:The rectangles in the graph below illustrate a right endpoint Riemann sum for \( f(x) = \frac{15}{x} \) on the interval \([3, 7]\).
The value of this right endpoint Riemann sum is \(\_\_\_\_\_\_\_\_\_\_\_\), and this Riemann sum is \([ \text{select an answer} ]\) the area of the region enclosed by \( y = f(x) \), the x-axis, and the vertical lines \( x = 3 \) and \( x = 7 \).
**Graph Explanation:**
The graph displays the function \( f(x) = \frac{15}{x} \) with a curve descending from left to right. Blue rectangles are used to approximate the area under the curve from \( x = 3 \) to \( x = 7 \). These rectangles represent the right endpoint Riemann sum, where the height of each rectangle is determined by the function value at the right endpoint of each subinterval. The x-axis is labeled from 3 to 7, and the y-axis has values labeled from 0 to 9.
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