Estimate L4 and R4 over [0, 7] for the function f(x) = 5x². (Use decimal notation. Give your answers to three decimal places.)
Estimate L4 and R4 over [0, 7] for the function f(x) = 5x². (Use decimal notation. Give your answers to three decimal places.)
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
![**Mathematical Problem: Estimating Integrals**
Estimate \( L_4 \) and \( R_4 \) over the interval \([0, 7]\) for the function \( f(x) = 5x^2 \).
*(Use decimal notation. Give your answers to three decimal places.)*
---
**Explanation:**
In this problem, \( L_4 \) and \( R_4 \) represent numerical approximations of the definite integral of the function \( f(x) = 5x^2 \) over the interval \([0, 7]\). The subscripts indicate that the interval is divided into 4 equal subintervals.
- \( L_4 \): Left-hand sum approximation.
- \( R_4 \): Right-hand sum approximation.
These approximations involve summing the areas of rectangles under the curve, using either the left or right endpoints of each subinterval. The results should be presented to three decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb3d87c9-3c7a-4527-95ca-8f02768b6dfc%2F97c69613-0c34-4e9d-9b08-764ea796b351%2Fia1flld_processed.png&w=3840&q=75)
Transcribed Image Text:**Mathematical Problem: Estimating Integrals**
Estimate \( L_4 \) and \( R_4 \) over the interval \([0, 7]\) for the function \( f(x) = 5x^2 \).
*(Use decimal notation. Give your answers to three decimal places.)*
---
**Explanation:**
In this problem, \( L_4 \) and \( R_4 \) represent numerical approximations of the definite integral of the function \( f(x) = 5x^2 \) over the interval \([0, 7]\). The subscripts indicate that the interval is divided into 4 equal subintervals.
- \( L_4 \): Left-hand sum approximation.
- \( R_4 \): Right-hand sum approximation.
These approximations involve summing the areas of rectangles under the curve, using either the left or right endpoints of each subinterval. The results should be presented to three decimal places.
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