Sketch the region of integration, reverse the order of integration, and evaluate the integral. 2√In 2 √In 2 S S 7² dxdy 0 y/2 Choose the correct graph below. A. 2√In 2 √In 2 S S Tex²0 B. dydx 2√In 2 Ó √In 2 What is an equivalent double integral with the order of integration reversed? O C. √√In 2 0 2√√In 2
Sketch the region of integration, reverse the order of integration, and evaluate the integral. 2√In 2 √In 2 S S 7² dxdy 0 y/2 Choose the correct graph below. A. 2√In 2 √In 2 S S Tex²0 B. dydx 2√In 2 Ó √In 2 What is an equivalent double integral with the order of integration reversed? O C. √√In 2 0 2√√In 2
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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![### Double Integral and Region of Integration
**Problem Statement:**
Sketch the region of integration, reverse the order of integration, and evaluate the integral:
\[ \int_{0}^{2/\sqrt{\ln 2}} \int_{y/2}^{\sqrt{\ln 2}} 7e^{x^2} \, dx \, dy \]
---
**Graph Selection:**
Choose the correct graph below.
- **Option A:** Incorrect
- **Option B:** Correct (Selected)
- **Option C:** Incorrect
*Explanation of Graph (Correct Answer - B):*
The graph demonstrates the region of integration in the xy-plane.
- The region is bounded by the line \( x = \frac{y}{2} \) and \( x = \sqrt{\ln 2} \).
- The vertical bounds are from \( y = 0 \) to \( y = 2/\sqrt{\ln 2} \).
---
**Equivalent Reversed Order Integral:**
What is an equivalent double integral with the order of integration reversed?
\[ \int_{\Box}^{\Box} \int_{\Box}^{\Box} 7e^{x^2} \, dy \, dx \]
Filling in the boxes for the reverse order of integration:
\[ \int_{0}^{\sqrt{\ln 2}} \int_{0}^{2x} 7e^{x^2} \, dy \, dx \]
\<Note: Use the correct integration limits based on the region's boundaries after reversing the order of integration\>
**Summary:**
1. The original integral is given as:
\[ \int_{0}^{2/\sqrt{\ln 2}} \int_{y/2}^{\sqrt{\ln 2}} 7e^{x^2} \, dx \, dy \]
2. The correct graph representing the region of integration is *Option B*.
3. The equivalent double integral with the order of integration reversed is:
\[ \int_{0}^{\sqrt{\ln 2}} \int_{0}^{2x} 7e^{x^2} \, dy \, dx \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb21cc1b3-0a4b-474e-87d5-2a9f16683342%2F6462d09e-104f-4f5a-929c-79bf2c3ceeb7%2Fhxsn5ck_processed.png&w=3840&q=75)
Transcribed Image Text:### Double Integral and Region of Integration
**Problem Statement:**
Sketch the region of integration, reverse the order of integration, and evaluate the integral:
\[ \int_{0}^{2/\sqrt{\ln 2}} \int_{y/2}^{\sqrt{\ln 2}} 7e^{x^2} \, dx \, dy \]
---
**Graph Selection:**
Choose the correct graph below.
- **Option A:** Incorrect
- **Option B:** Correct (Selected)
- **Option C:** Incorrect
*Explanation of Graph (Correct Answer - B):*
The graph demonstrates the region of integration in the xy-plane.
- The region is bounded by the line \( x = \frac{y}{2} \) and \( x = \sqrt{\ln 2} \).
- The vertical bounds are from \( y = 0 \) to \( y = 2/\sqrt{\ln 2} \).
---
**Equivalent Reversed Order Integral:**
What is an equivalent double integral with the order of integration reversed?
\[ \int_{\Box}^{\Box} \int_{\Box}^{\Box} 7e^{x^2} \, dy \, dx \]
Filling in the boxes for the reverse order of integration:
\[ \int_{0}^{\sqrt{\ln 2}} \int_{0}^{2x} 7e^{x^2} \, dy \, dx \]
\<Note: Use the correct integration limits based on the region's boundaries after reversing the order of integration\>
**Summary:**
1. The original integral is given as:
\[ \int_{0}^{2/\sqrt{\ln 2}} \int_{y/2}^{\sqrt{\ln 2}} 7e^{x^2} \, dx \, dy \]
2. The correct graph representing the region of integration is *Option B*.
3. The equivalent double integral with the order of integration reversed is:
\[ \int_{0}^{\sqrt{\ln 2}} \int_{0}^{2x} 7e^{x^2} \, dy \, dx \]
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