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
Problem 1RQ
Related questions
Topic Video
Question
Could you please help me answer this? Thank you
![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.)
\[ A_{\text{right}} = \underline{\hspace{5cm}} \]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
