Let R be the region in the figure below. What can we say about the numerical value of It is positive It is negative It is zero ру It is not a real number. SSR e¯(²x²+³y²) dA? 7+
Let R be the region in the figure below. What can we say about the numerical value of It is positive It is negative It is zero ру It is not a real number. SSR e¯(²x²+³y²) dA? 7+
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Let \( R \) be the region in the figure below.**
The diagram shows a curvilinear region \( R \) in a plane with the \( x \)-axis and \( y \)-axis labeled. The shape looks like a twisted or curvy worm, filled with green dots, and is bounded mostly smoothly along its edges. The region is marked with the letter \( R \).
**What can we say about the numerical value of**
\[
\iint_R e^{-(2x^2 + 3y^2)} \, dA?
\]
- ○ It is positive
- ○ It is negative
- ○ It is zero
- ○ It is not a real number
The question prompts an evaluation of the integral over the region \( R \) for the function \( e^{-(2x^2 + 3y^2)} \), using the differential area element \( dA \). The options suggest considering characteristics such as sign and reality of the integral's value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72514fec-ab1d-4e58-a749-feb22f2ce6e9%2Fed34d47f-27dc-4458-b975-5c77e99e7350%2F5hnafv_processed.png&w=3840&q=75)
Transcribed Image Text:**Let \( R \) be the region in the figure below.**
The diagram shows a curvilinear region \( R \) in a plane with the \( x \)-axis and \( y \)-axis labeled. The shape looks like a twisted or curvy worm, filled with green dots, and is bounded mostly smoothly along its edges. The region is marked with the letter \( R \).
**What can we say about the numerical value of**
\[
\iint_R e^{-(2x^2 + 3y^2)} \, dA?
\]
- ○ It is positive
- ○ It is negative
- ○ It is zero
- ○ It is not a real number
The question prompts an evaluation of the integral over the region \( R \) for the function \( e^{-(2x^2 + 3y^2)} \), using the differential area element \( dA \). The options suggest considering characteristics such as sign and reality of the integral's value.
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