Evaluate the definite integral by the limit definition. [²5 Step 1 5 dx To find the definite integral Then the width of each interval is Ax = Note that ||A|| L² 5 dx by the limit definition, divide the interval [4, 9] into n subintervals. n 5 b-a n X Submit Skip (you cannot come back) n 9-4 as n → ∞o.
Evaluate the definite integral by the limit definition. [²5 Step 1 5 dx To find the definite integral Then the width of each interval is Ax = Note that ||A|| L² 5 dx by the limit definition, divide the interval [4, 9] into n subintervals. n 5 b-a n X Submit Skip (you cannot come back) n 9-4 as n → ∞o.
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
![**Evaluating Definite Integrals Using the Limit Definition**
To evaluate the definite integral by the limit definition:
\[
\int_{4}^{9} 5\, dx
\]
### Step 1
To find the definite integral \(\int_{4}^{9} 5\, dx\) using the limit definition, divide the interval \([4, 9]\) into \(n\) subintervals.
### Calculating the Width of Each Interval
The width of each interval, \(\Delta x\), can be calculated as:
\[
\Delta x = \frac{b - a}{n} = \frac{9 - 4}{n}
\]
This simplifies to:
\[
\Delta x = \frac{5}{n}
\]
### Note
As \(n \to \infty\), \(\|\Delta\|\) approaches 0.
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Transcribed Image Text:**Evaluating Definite Integrals Using the Limit Definition**
To evaluate the definite integral by the limit definition:
\[
\int_{4}^{9} 5\, dx
\]
### Step 1
To find the definite integral \(\int_{4}^{9} 5\, dx\) using the limit definition, divide the interval \([4, 9]\) into \(n\) subintervals.
### Calculating the Width of Each Interval
The width of each interval, \(\Delta x\), can be calculated as:
\[
\Delta x = \frac{b - a}{n} = \frac{9 - 4}{n}
\]
This simplifies to:
\[
\Delta x = \frac{5}{n}
\]
### Note
As \(n \to \infty\), \(\|\Delta\|\) approaches 0.
Buttons at the bottom:
- **Submit**
- **Skip (you cannot come back)**
Expert Solution
Step 1: Divide the interval into n subintervals and length of the each subintervals.
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