Evaluate the definite integral by the limit definition. '6 Lox³ dx
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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![**Evaluate the Definite Integral by the Limit Definition**
\[
\int_{-6}^{6} x^3 \, dx
\]
**Step 1**
To find the definite integral \(\int_{-6}^{6} x^3 \, dx\) by the limit definition, divide the interval \([-6, 6]\) into \(n\) subintervals.
Then the width of each interval is
\[
\Delta x = \frac{b - a}{n}
\]
\[
= \frac{6 - (-6)}{n}
\]
\[
= \frac{12}{n}
\]
Note that \(\|\Delta\|\rightarrow 0\) as \(n \rightarrow \infty\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab6702de-5579-4c14-bacb-4d8e7e421acd%2F0697648d-3b4d-4191-b57a-58aa933a21bb%2Foataxsg_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate the Definite Integral by the Limit Definition**
\[
\int_{-6}^{6} x^3 \, dx
\]
**Step 1**
To find the definite integral \(\int_{-6}^{6} x^3 \, dx\) by the limit definition, divide the interval \([-6, 6]\) into \(n\) subintervals.
Then the width of each interval is
\[
\Delta x = \frac{b - a}{n}
\]
\[
= \frac{6 - (-6)}{n}
\]
\[
= \frac{12}{n}
\]
Note that \(\|\Delta\|\rightarrow 0\) as \(n \rightarrow \infty\).
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Follow-up Question
![**Evaluate the definite integral by the limit definition.**
\[
\int_{-6}^{6} x^3 \, dx
\]
**Step 1**
To find the definite integral \(\int_{-6}^{6} x^3 \, dx\) by the limit definition, divide the interval \([-6, 6]\) into \(n\) subintervals.
Then the width of each interval is
\[
\Delta x = \frac{b-a}{n}
\]
\[
= \frac{6 - (-6)}{n}
\]
\[
= \frac{12}{n}
\]
Note that \(\|\Delta l\| \to 0\) as \(n \to \infty\).
**Buttons:**
- Submit
- Skip (you cannot come back)](https://content.bartleby.com/qna-images/question/ab6702de-5579-4c14-bacb-4d8e7e421acd/717da0c1-dfbb-48b2-bd8f-a694fd036d1d/7k8zsns_processed.png)
Transcribed Image Text:**Evaluate the definite integral by the limit definition.**
\[
\int_{-6}^{6} x^3 \, dx
\]
**Step 1**
To find the definite integral \(\int_{-6}^{6} x^3 \, dx\) by the limit definition, divide the interval \([-6, 6]\) into \(n\) subintervals.
Then the width of each interval is
\[
\Delta x = \frac{b-a}{n}
\]
\[
= \frac{6 - (-6)}{n}
\]
\[
= \frac{12}{n}
\]
Note that \(\|\Delta l\| \to 0\) as \(n \to \infty\).
**Buttons:**
- Submit
- Skip (you cannot come back)
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