Find the area of the plane z = 4x+y for all (x,y) ∈ R where R is the region in the first quadrant which is bounded by the circle r = 4sin(θ) and the lemniscate r = ?8 cos (2θ) both given in polar coordinates

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
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Find the area of the plane z = 4x+y for all (x,y) ∈ R where R is the region in the first quadrant which is bounded by the circle r = 4sin(θ) and the lemniscate r = ?8 cos (2θ) both given in polar coordinates
4. Find the area of the plane z = 4r + y for all (r, y) eR where R is the region
in the first quadrant which is bounded by the circler = 4sin (0) and the
lemniscate r = V8 cos (20) both given in polar coordinates.
2
az
A(S) =
1+
dA,
16 of 30
where R is the domain over which we are interested to find the area of the
surface z. Sketch the region R before doing the integration. (In polar
coordinates, dA = rdrd0)
Transcribed Image Text:4. Find the area of the plane z = 4r + y for all (r, y) eR where R is the region in the first quadrant which is bounded by the circler = 4sin (0) and the lemniscate r = V8 cos (20) both given in polar coordinates. 2 az A(S) = 1+ dA, 16 of 30 where R is the domain over which we are interested to find the area of the surface z. Sketch the region R before doing the integration. (In polar coordinates, dA = rdrd0)
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