Estimate the area under the graph of f(x) = x² +5 over the interval [0, 10] using 10 approximating rectangles and midpoints as sample points. M10 = Repeat the approximation using using 50 approximating rectangles. M50 = Repeat the approximation using using 100 approximating rectangles. M100 = Repeat the approximation using using 500 approximating rectangles. M500 = These consecutive approximations appear to be approaching what value? So, it appears that the following integral expression is valid: S dr =
Estimate the area under the graph of f(x) = x² +5 over the interval [0, 10] using 10 approximating rectangles and midpoints as sample points. M10 = Repeat the approximation using using 50 approximating rectangles. M50 = Repeat the approximation using using 100 approximating rectangles. M100 = Repeat the approximation using using 500 approximating rectangles. M500 = These consecutive approximations appear to be approaching what value? So, it appears that the following integral expression is valid: S dr =
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Estimating the Area Under a Curve
#### Problem Statement
Estimate the area under the graph of \( f(x) = x^2 + 5 \) over the interval \([0, 10]\) using approximating rectangles with midpoints as sample points.
#### Calculations
1. **Using 10 Approximating Rectangles:**
\[
M_{10} = \text{[Enter Calculation Here]}
\]
2. **Using 50 Approximating Rectangles:**
\[
M_{50} = \text{[Enter Calculation Here]}
\]
3. **Using 100 Approximating Rectangles:**
\[
M_{100} = \text{[Enter Calculation Here]}
\]
4. **Using 500 Approximating Rectangles:**
\[
M_{500} = \text{[Enter Calculation Here]}
\]
#### Observations
These consecutive approximations appear to be approaching what value?
\[
\text{[Approaching Value]}
\]
#### Integral Expression
So, it appears that the following integral expression is valid:
\[
\int_{0}^{10} (x^2 + 5) \, dx = \text{[Enter Exact Value]}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b638ef2-9928-44ee-907b-a6bc7b9add08%2Fd39ebfa7-0ea4-4923-9179-75e976790629%2Fnwa14rk_processed.png&w=3840&q=75)
Transcribed Image Text:### Estimating the Area Under a Curve
#### Problem Statement
Estimate the area under the graph of \( f(x) = x^2 + 5 \) over the interval \([0, 10]\) using approximating rectangles with midpoints as sample points.
#### Calculations
1. **Using 10 Approximating Rectangles:**
\[
M_{10} = \text{[Enter Calculation Here]}
\]
2. **Using 50 Approximating Rectangles:**
\[
M_{50} = \text{[Enter Calculation Here]}
\]
3. **Using 100 Approximating Rectangles:**
\[
M_{100} = \text{[Enter Calculation Here]}
\]
4. **Using 500 Approximating Rectangles:**
\[
M_{500} = \text{[Enter Calculation Here]}
\]
#### Observations
These consecutive approximations appear to be approaching what value?
\[
\text{[Approaching Value]}
\]
#### Integral Expression
So, it appears that the following integral expression is valid:
\[
\int_{0}^{10} (x^2 + 5) \, dx = \text{[Enter Exact Value]}
\]
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