(a) Estimate the area under the graph of f(x) = 4/x from x = 1 to x = 5 using four approximating rectangles and right endpoints. R4 = (b) Repeat part (a) using left endpoints. L4 = (c) By looking at a sketch of the graph and the rectangles, determine for each estimate whether is overestimates, underestimates, or is the exact area. Underestimate 1. L4 2. R4 Exact
(a) Estimate the area under the graph of f(x) = 4/x from x = 1 to x = 5 using four approximating rectangles and right endpoints. R4 = (b) Repeat part (a) using left endpoints. L4 = (c) By looking at a sketch of the graph and the rectangles, determine for each estimate whether is overestimates, underestimates, or is the exact area. Underestimate 1. L4 2. R4 Exact
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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![### Estimating the Area under a Curve
#### (a) Estimate the Area Using Right Endpoints
To estimate the area under the graph of \( f(x) = \frac{4}{x} \) from \( x = 1 \) to \( x = 5 \) using four approximating rectangles and right endpoints:
\[ R_4 = \]
#### (b) Repeat the Estimation Using Left Endpoints
To estimate the area under the same graph using left endpoints:
\[ L_4 = \]
#### (c) Determine the Accuracy of Each Estimate
By looking at a sketch of the graph and the rectangles, determine for each estimate whether it is an overestimate, underestimate, or the exact area.
**Underestimate**
\[ 1. \quad L_4 \]
**Exact**
\[ 2. \quad R_4 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5e88e6-b1af-4aea-9b08-2dadd85f5e2c%2F2b2366c7-1234-48d6-8c84-819989c51475%2Fqbaoblm_processed.png&w=3840&q=75)
Transcribed Image Text:### Estimating the Area under a Curve
#### (a) Estimate the Area Using Right Endpoints
To estimate the area under the graph of \( f(x) = \frac{4}{x} \) from \( x = 1 \) to \( x = 5 \) using four approximating rectangles and right endpoints:
\[ R_4 = \]
#### (b) Repeat the Estimation Using Left Endpoints
To estimate the area under the same graph using left endpoints:
\[ L_4 = \]
#### (c) Determine the Accuracy of Each Estimate
By looking at a sketch of the graph and the rectangles, determine for each estimate whether it is an overestimate, underestimate, or the exact area.
**Underestimate**
\[ 1. \quad L_4 \]
**Exact**
\[ 2. \quad R_4 \]
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