Calculate by changing to polar coordinates. а) О 3пе4 - 3п - b) 0-3пе-4 + 3 3п c) 0-6пе d) O e) ( Зп 2 Зп + 6п + Зп 2 Зп 2 f) ( None of these. LLD needs СМ 3 e-(z²+y²) dx dy
Calculate by changing to polar coordinates. а) О 3пе4 - 3п - b) 0-3пе-4 + 3 3п c) 0-6пе d) O e) ( Зп 2 Зп + 6п + Зп 2 Зп 2 f) ( None of these. LLD needs СМ 3 e-(z²+y²) dx dy
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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![**Question 7**
Calculate by changing to polar coordinates.
\[
\int_{2}^{2} \int_{\sqrt{4-y^2}}^{\sqrt{4-y^2}} 3e^{-(x^2+y^2)} \, dx \, dy
\]
a) \(3\pi e^4 - 3\pi\)
b) \(-3\pi e^{-4} + 3\pi\)
c) \(-6\pi e^{-4} + 6\pi\)
d) \(3\pi e^{-4} + \frac{3\pi}{2}\)
e) \(\frac{3\pi}{2} e^4 - \frac{3\pi}{2}\)
f) None of these.
---
**Question 8**
Use a double integral to find the area of the region outside the circle \(r = 3\) but inside the circle \(r = 4\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3ec8c1d-50e8-44c3-be61-249610e2bef3%2F01f41db1-4553-4320-a10d-5db518670e03%2Fzhaly7j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 7**
Calculate by changing to polar coordinates.
\[
\int_{2}^{2} \int_{\sqrt{4-y^2}}^{\sqrt{4-y^2}} 3e^{-(x^2+y^2)} \, dx \, dy
\]
a) \(3\pi e^4 - 3\pi\)
b) \(-3\pi e^{-4} + 3\pi\)
c) \(-6\pi e^{-4} + 6\pi\)
d) \(3\pi e^{-4} + \frac{3\pi}{2}\)
e) \(\frac{3\pi}{2} e^4 - \frac{3\pi}{2}\)
f) None of these.
---
**Question 8**
Use a double integral to find the area of the region outside the circle \(r = 3\) but inside the circle \(r = 4\).
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