Estimate the area of the shaded region in the graph by using the Trapezoidal Rule with n=4. A Select the correct answer.
Estimate the area of the shaded region in the graph by using the Trapezoidal Rule with n=4. A Select the correct answer.
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 Using the Trapezoidal Rule
**Problem Statement:**
Estimate the area of the shaded region in the graph by using the Trapezoidal Rule with \( n = 4 \).
**Graph Description:**
The provided graph shows a curve with a shaded region beneath it. The curve peaks towards the center and tapers off symmetrically on either side. The grid under the graph helps in better visual estimation and precise calculation of the area beneath the curve.
**Calculation Approach:**
To estimate the area under the curve using the Trapezoidal Rule with \( n = 4 \) means that the interval under the curve is divided into 4 equal parts. The area is then approximated by calculating the area of the trapezoids formed under the curve within these intervals.
**Choices:**
Select the correct answer for the estimated area:
- [ ] 12
- [ ] 10.5
- [ ] 6.9
- [ ] 8.5
- [ ] 7.4
- [ ] 12.5
### Educational Notes:
The Trapezoidal Rule is a numerical method used to approximate the definite integral of a function. It works by approximating the region under the curve as a series of trapezoids, calculating their areas, and summing them. This method provides a more accurate estimation than simple rectangular approximations, especially for functions that are not linear.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24e8bfde-46ac-4815-81bc-d8be1d9c4f35%2F50fa0228-5d5c-4924-9c3d-16e44ab0baa6%2Fct87ip_processed.png&w=3840&q=75)
Transcribed Image Text:### Estimating the Area Using the Trapezoidal Rule
**Problem Statement:**
Estimate the area of the shaded region in the graph by using the Trapezoidal Rule with \( n = 4 \).
**Graph Description:**
The provided graph shows a curve with a shaded region beneath it. The curve peaks towards the center and tapers off symmetrically on either side. The grid under the graph helps in better visual estimation and precise calculation of the area beneath the curve.
**Calculation Approach:**
To estimate the area under the curve using the Trapezoidal Rule with \( n = 4 \) means that the interval under the curve is divided into 4 equal parts. The area is then approximated by calculating the area of the trapezoids formed under the curve within these intervals.
**Choices:**
Select the correct answer for the estimated area:
- [ ] 12
- [ ] 10.5
- [ ] 6.9
- [ ] 8.5
- [ ] 7.4
- [ ] 12.5
### Educational Notes:
The Trapezoidal Rule is a numerical method used to approximate the definite integral of a function. It works by approximating the region under the curve as a series of trapezoids, calculating their areas, and summing them. This method provides a more accurate estimation than simple rectangular approximations, especially for functions that are not linear.
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