Consider the polar curves C1 : r = 4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2) cos θ 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 θ increases on the interval [0, 2π]. Also, for each of these curves, r > 0 when θ ∈ [0, 2π]. _ 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
Consider the polar curves C1 : r = 4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2) cos θ 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 θ increases on the interval [0, 2π]. Also, for each of these curves, r > 0 when θ ∈ [0, 2π]. _ 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
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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Consider the polar curves C1 : r = 4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2) cos θ 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 θ increases on the interval [0, 2π].
Also, for each of these curves, r > 0 when θ ∈ [0, 2π].
_ 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
Transcribed Image Text:P
π
2
R
C₂
C₁
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