f(x) = x2 between x = 4 and x 8 using the midpoint sum with four rectangles of equal width. 165 174 126 149
f(x) = x2 between x = 4 and x 8 using the midpoint sum with four rectangles of equal width. 165 174 126 149
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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Question
![The problem statement reads:
"Find the approximate value of the integral of the function \( f(x) = x^2 \) between \( x = 4 \) and \( x = 8 \) using the midpoint sum method with four rectangles of equal width."
Options are given as:
- 165
- 174
- 126
- 149
The task involves calculating the area under the curve \( y = x^2 \) over the interval [4, 8] using the midpoint rule with four subdivisions. Each rectangle's width is calculated as \((8-4)/4 = 1\). The function \( f(x) \) is evaluated at the midpoints of each interval to approximate the integral.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4551f2ef-4c78-4d27-9320-7cb594875026%2F1be2e303-e715-43bc-b45a-3d26931fde12%2F4igtjwk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem statement reads:
"Find the approximate value of the integral of the function \( f(x) = x^2 \) between \( x = 4 \) and \( x = 8 \) using the midpoint sum method with four rectangles of equal width."
Options are given as:
- 165
- 174
- 126
- 149
The task involves calculating the area under the curve \( y = x^2 \) over the interval [4, 8] using the midpoint rule with four subdivisions. Each rectangle's width is calculated as \((8-4)/4 = 1\). The function \( f(x) \) is evaluated at the midpoints of each interval to approximate the integral.
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