In the graph, f(1) = 21, f(2) = 13, f(3) = 9, f(4) = 4. (1,f1)) y-f(x) (2.f(2)) (3.Л3) (4. f4)) 3 4 (a) Approximate the shaded area under the graph of f by constructing rectangles using the left endpoint of each subinterval. (Use symbolic notation and fractions where needed.) Ateft = (b) Approximate the shaded area under the graph of f by constructing rectangles using the right endpoint of each subinterval.
In the graph, f(1) = 21, f(2) = 13, f(3) = 9, f(4) = 4. (1,f1)) y-f(x) (2.f(2)) (3.Л3) (4. f4)) 3 4 (a) Approximate the shaded area under the graph of f by constructing rectangles using the left endpoint of each subinterval. (Use symbolic notation and fractions where needed.) Ateft = (b) Approximate the shaded area under the graph of f by constructing rectangles using the right endpoint of each subinterval.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![In the graph, \( f(1) = 21 \), \( f(2) = 13 \), \( f(3) = 9 \), \( f(4) = 4 \).
### Diagram Explanation
The graph provided depicts a curve of the function \( y = f(x) \). There are four points marked on the graph: \( (1, f(1)) \), \( (2, f(2)) \), \( (3, f(3)) \), and \( (4, f(4)) \). The shaded area under the curve between these points is divided into three subintervals, each represented by rectangles. The tops of these rectangles align with the function's value at the left endpoint of each subinterval, illustrating a left Riemann sum approximation.
### Problem Statement
(a) **Approximate the shaded area under the graph of \( f \) by constructing rectangles using the left endpoint of each subinterval.**
(Use symbolic notation and fractions where needed.)
\[ A_{\text{left}} = \]
(b) **Approximate the shaded area under the graph of \( f \) by constructing rectangles using the right endpoint of each subinterval.**
The task requires calculating the area under the graph as a numerical approximation, providing a visual and analytical understanding of integral approximations using Riemann sums.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08156d39-b854-45f2-9d90-7fd147414e14%2F8ee8891c-c0b6-437e-bceb-1755e4ff24cd%2Fgi95suh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the graph, \( f(1) = 21 \), \( f(2) = 13 \), \( f(3) = 9 \), \( f(4) = 4 \).
### Diagram Explanation
The graph provided depicts a curve of the function \( y = f(x) \). There are four points marked on the graph: \( (1, f(1)) \), \( (2, f(2)) \), \( (3, f(3)) \), and \( (4, f(4)) \). The shaded area under the curve between these points is divided into three subintervals, each represented by rectangles. The tops of these rectangles align with the function's value at the left endpoint of each subinterval, illustrating a left Riemann sum approximation.
### Problem Statement
(a) **Approximate the shaded area under the graph of \( f \) by constructing rectangles using the left endpoint of each subinterval.**
(Use symbolic notation and fractions where needed.)
\[ A_{\text{left}} = \]
(b) **Approximate the shaded area under the graph of \( f \) by constructing rectangles using the right endpoint of each subinterval.**
The task requires calculating the area under the graph as a numerical approximation, providing a visual and analytical understanding of integral approximations using Riemann sums.
![(b) Approximate the shaded area under the graph of \( f \) by constructing rectangles using the right endpoint of each subinterval.
(Use symbolic notation and fractions where needed.)
\[ A_{\text{right}} = \underline{\hspace{5cm}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08156d39-b854-45f2-9d90-7fd147414e14%2F8ee8891c-c0b6-437e-bceb-1755e4ff24cd%2Fk273oh3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) Approximate the shaded area under the graph of \( f \) by constructing rectangles using the right endpoint of each subinterval.
(Use symbolic notation and fractions where needed.)
\[ A_{\text{right}} = \underline{\hspace{5cm}} \]
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