3√2 √2 cos 2 2 Consider the polar curves C₁ : r = 4+² cos 0 and C₂ r = 2- as shown in the figure on the right. The curves C₁ and C₂ are both symmetric with respect to the polar axis. Each of these curves is traced counterclockwise as the value of increases on the interval [0, 2π]. Also, for each of these curves, r> 0 when 0 € [0, 2π]. P 1. Let P be the point of intersection of C₁ and C₂ in the second quad- rant. Find polar coordinates (r, 0) for the point P where r > 0 and 0 € [0, 2π]. 2. Let R be the region that is inside both C₁ and C₂. Set up, but do not evaluate, the integral or sum of integrals for the following: (a) the area of R (b) the perimeter of R π NIV R C₂ 0
3√2 √2 cos 2 2 Consider the polar curves C₁ : r = 4+² cos 0 and C₂ r = 2- as shown in the figure on the right. The curves C₁ and C₂ are both symmetric with respect to the polar axis. Each of these curves is traced counterclockwise as the value of increases on the interval [0, 2π]. Also, for each of these curves, r> 0 when 0 € [0, 2π]. P 1. Let P be the point of intersection of C₁ and C₂ in the second quad- rant. Find polar coordinates (r, 0) for the point P where r > 0 and 0 € [0, 2π]. 2. Let R be the region that is inside both C₁ and C₂. Set up, but do not evaluate, the integral or sum of integrals for the following: (a) the area of R (b) the perimeter of R π NIV R C₂ 0
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
![3√2
√2
2
2
Consider the polar curves C₁ : r = 4+· cos 0 and C₂ r = 2-- cos
as shown in the figure on the right. The curves C₁ and C₂ are both
symmetric with respect to the polar axis. Each of these curves is traced
counterclockwise as the value of increases on the interval [0, 2π]. Also,
for each of these curves, r> 0 when 0 = [0,27].
P
1. Let P be the point of intersection of C₁ and C₂ in the second quad-
rant. Find polar coordinates (r, 0) for the point P where r > 0 and
θε[0, 2π].
2. Let R be the region that is inside both C₁ and C₂. Set up, but
do not evaluate, the integral or sum of integrals for the following:
(a) the area of R
(b) the perimeter of R
NIE
π
R
C₂
C₁](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b9c5b92-db4e-476d-a20e-7471ecf5b6a2%2F18ab9fb2-c48b-4275-a6cf-4fb0ebbedcd9%2Fa94ctu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3√2
√2
2
2
Consider the polar curves C₁ : r = 4+· cos 0 and C₂ r = 2-- cos
as shown in the figure on the right. The curves C₁ and C₂ are both
symmetric with respect to the polar axis. Each of these curves is traced
counterclockwise as the value of increases on the interval [0, 2π]. Also,
for each of these curves, r> 0 when 0 = [0,27].
P
1. Let P be the point of intersection of C₁ and C₂ in the second quad-
rant. Find polar coordinates (r, 0) for the point P where r > 0 and
θε[0, 2π].
2. Let R be the region that is inside both C₁ and C₂. Set up, but
do not evaluate, the integral or sum of integrals for the following:
(a) the area of R
(b) the perimeter of R
NIE
π
R
C₂
C₁
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