Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement: Evaluate the Double Integral**
Find the value of the following double integral:
\[
\int_{1}^{2} \int_{4}^{6} xy \, dy \, dx.
\]
---
**Explanation of the Problem:**
This is a problem related to evaluating a double integral over a specified region.
**Steps to Evaluate:**
1. **Inner Integral:**
- Consider the inner integral \(\int_{4}^{6} xy \, dy\).
- Treat \(x\) as a constant, and integrate with respect to \(y\).
2. **Outer Integral:**
- After finding the result of the inner integral, proceed to evaluate the outer integral \(\int_{1}^{2} (\text{result of inner integral}) \, dx\).
3. **Combine Results:**
- The final answer will be the result of these integrals combined, representing the cumulative value over the given range in both variables.
This exercise requires familiarity with the techniques of integration, including the basic rules for integrating polynomial expressions and applying the limits of integration.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8216494-bf6c-44b6-949f-dd8ff9f3594a%2F5a817c38-c130-4811-a417-6da151c08ddc%2Fh21ozlp_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Evaluate the Double Integral**
Find the value of the following double integral:
\[
\int_{1}^{2} \int_{4}^{6} xy \, dy \, dx.
\]
---
**Explanation of the Problem:**
This is a problem related to evaluating a double integral over a specified region.
**Steps to Evaluate:**
1. **Inner Integral:**
- Consider the inner integral \(\int_{4}^{6} xy \, dy\).
- Treat \(x\) as a constant, and integrate with respect to \(y\).
2. **Outer Integral:**
- After finding the result of the inner integral, proceed to evaluate the outer integral \(\int_{1}^{2} (\text{result of inner integral}) \, dx\).
3. **Combine Results:**
- The final answer will be the result of these integrals combined, representing the cumulative value over the given range in both variables.
This exercise requires familiarity with the techniques of integration, including the basic rules for integrating polynomial expressions and applying the limits of integration.
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