. Using Green's theorem, show that the area of a plane region in polar coordinate is 1 $ C r²do. Hence, find the area of cardioid r = a(1- cos 0), a > 0.

Q: The area enclosed inside the polar curve r² = 14cos(20) is Select one: a. 28 O b. 14 O c. 14元 O d.…

A: The correct option is b. The area is 14 unit squared.Explanation:Kindly see attached photo for your…

Q: Consider the polar curves C: R = 2 – cos e and C2:r = 2+2 cos 0, 6 € [0,2) • Show that both C, and…

A: Given equation of polar curves are: R=2-cos θr=2+2cos θ

Q: Consider the polar curves C₁: r = 3 (blue) and C₂:r = 2 – 2sin0 (red) and let R be the shaded region…

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Q: Let R be the region in the first, third, and fourth quadrants that is inside the polar curve r = 1 -…

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Q: Find the area enclosed by the polar curve 36 r2 4 cos? 0 +9 sin² e 2 Select one: O a. 10pi O b. 6pi…

A: In a polar coordinate system a point of the plane is represented by a pair of two numbers (r,θ). The…

Q: Find plane area inside polar function r 2 and outside polar function r= -2sint in thisd quurter.

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Q: Sketch the graph and set up the integral of the area of: a). Inside r1, but outside r2 b). Inside…

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Q: Use pola

A: Introduction: To convert the rectangular coordinates x,y into the polar coordinates r,θ, we have,…

Q: 3. the first quadrant area bounded by the curve r=a sin 2 0

A: Double integral is used to integrate the function of two variable over two dimensional region.…

Q: ) Evaluate √x² + y²dA where D is the region bounded by the polar curve r = 2 cos. Sketch the region.…

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Q: Let D be the overlap part of the three planar regions each bounded by closed polar curves r = 1, r =…

A: Here given that D is overlap of the three regions each bounded by closed polar curves (a)

Q: 2. Consider the polar curves C,:r= 8cos(20) and Ca:r = 4v2 Cir=4V2 Cir=8 cos(20) 10 12 14 10 a. Find…

A: The polar curves are given as , C1:r=8cos2θ and C2:r=42

Q: For the polar equations r1=1-cosx and r2=1, (1)sketch the graphs of r1 and r2 in the same coordinate…

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Q: 3) Consider the polar functions r, = 0 and r, = 20 a) Sketch the area between the two spirals for 0…

A: When, r = θ   ; 0≤θ≤2πx = θ*cosθy = θ*sinθ theta (rad) theta (degrees) x = theta*cos(theta)…

Q: Two polar curves C, and C2 are given in the interval 0 < 0 <- respectively by: V2cos20 and r = Find…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 1)using polar coordinates, calculate (x + y)dA R where R is the region to the left of the axis…

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Q: 2. Consider the polar curves r = 4 - 2cosθ and r = 2 + 2cosθ. In this problem, we want to find the…

A: Given the polar curves,r1​=4−2cosθr2​=2+2cosθ (a) Solving for the intersection point between 2…

Q: Use polar coordinates to evaluate sin (a² + y²)* dA, R where R is the region enclosed by the curves…

A: Here if we put limits in order dr dθ, then the given integral can not b evaluated so we need to put…