Estimate L4 and R4 over [0, 3] for the function f(x) = 2x2. (Use decimal notation. Give your answers to three decimal places.)
Estimate L4 and R4 over [0, 3] for the function f(x) = 2x2. (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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![**Problem Statement:**
Estimate \( L_4 \) and \( R_4 \) over \([0,3]\) for the function \( f(x) = 2x^2 \).
(Use decimal notation. Give your answers to three decimal places.)
---
\[
L_4 \approx \underline{\hspace{3in}}
\]
\[
R_4 \approx \underline{\hspace{3in}}
\]
---
**Explanation:**
This problem requires the calculation of left and right Riemann sums with \( n = 4 \) partitions over the interval \([0,3]\) for the function \( f(x) = 2x^2 \).
- **Left Riemann Sum (\( L_4 \))**: Approximates the area under the curve using the left endpoints of the subintervals.
- **Right Riemann Sum (\( R_4 \))**: Approximates the area under the curve using the right endpoints of the subintervals.
The task is to complete these calculations and provide approximations to three decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9157ff54-bf1a-4493-8174-8933936166e8%2F6b1958e9-5398-481b-9b56-c2d2028345ae%2F1idlmpe_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Estimate \( L_4 \) and \( R_4 \) over \([0,3]\) for the function \( f(x) = 2x^2 \).
(Use decimal notation. Give your answers to three decimal places.)
---
\[
L_4 \approx \underline{\hspace{3in}}
\]
\[
R_4 \approx \underline{\hspace{3in}}
\]
---
**Explanation:**
This problem requires the calculation of left and right Riemann sums with \( n = 4 \) partitions over the interval \([0,3]\) for the function \( f(x) = 2x^2 \).
- **Left Riemann Sum (\( L_4 \))**: Approximates the area under the curve using the left endpoints of the subintervals.
- **Right Riemann Sum (\( R_4 \))**: Approximates the area under the curve using the right endpoints of the subintervals.
The task is to complete these calculations and provide approximations to three decimal places.
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