A table of values of a function f(x) is shown. Use the table to find Left-hand and Right-hand Riemann Sums with 5 subintervals of equal width. 10 15 20 25 f(x) -42 -37 -25 -6 15 36 Left-hand Sum Right-hand Sum =
A table of values of a function f(x) is shown. Use the table to find Left-hand and Right-hand Riemann Sums with 5 subintervals of equal width. 10 15 20 25 f(x) -42 -37 -25 -6 15 36 Left-hand Sum Right-hand Sum =
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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Based on the table, can you help me find left & right Riemann Sums?
![A table of values of a function \( f(x) \) is shown. Use the table to find Left-hand and Right-hand Riemann Sums with 5 subintervals of equal width.
\[
\begin{array}{c|ccccc}
x & 0 & 5 & 10 & 15 & 20 & 25 \\
\hline
f(x) & -42 & -37 & -25 & -6 & 15 & 36 \\
\end{array}
\]
**Left-hand Sum =** [Input Box]
**Right-hand Sum =** [Input Box]
**Explanation:**
To calculate the Left-hand Riemann Sum, use the formula based on the left endpoints of each interval. Similarly, the Right-hand Riemann Sum uses the right endpoints. Divide the interval [0, 25] into 5 equal subintervals. Each subinterval has a width of \( \Delta x = 5 \).
- **Left-hand Sum:** Use values \( f(0), f(5), f(10), f(15), f(20) \).
- **Right-hand Sum:** Use values \( f(5), f(10), f(15), f(20), f(25) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64493c82-ae9f-4de1-a1ce-9a1e251847f0%2F1fcdc828-2b67-4971-a66b-3d513afff685%2Fxgjiao3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A table of values of a function \( f(x) \) is shown. Use the table to find Left-hand and Right-hand Riemann Sums with 5 subintervals of equal width.
\[
\begin{array}{c|ccccc}
x & 0 & 5 & 10 & 15 & 20 & 25 \\
\hline
f(x) & -42 & -37 & -25 & -6 & 15 & 36 \\
\end{array}
\]
**Left-hand Sum =** [Input Box]
**Right-hand Sum =** [Input Box]
**Explanation:**
To calculate the Left-hand Riemann Sum, use the formula based on the left endpoints of each interval. Similarly, the Right-hand Riemann Sum uses the right endpoints. Divide the interval [0, 25] into 5 equal subintervals. Each subinterval has a width of \( \Delta x = 5 \).
- **Left-hand Sum:** Use values \( f(0), f(5), f(10), f(15), f(20) \).
- **Right-hand Sum:** Use values \( f(5), f(10), f(15), f(20), f(25) \).
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