Find the areas of the regions . 1. Shared by the circles r = 2 cos u and r = 2 sin u 2. Shared by the circles r = 1 and r = 2 sin u

Q: Use the Green’s Theorem area formula given above to find the areasof the regions enclosed by the…

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Q: Find the area of the region shared by the cardiods r=12(1+cosθ) and r=12(1-cosθ)

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Q: Find the area of the region that lies inside both of the circles; r=2cosθ r=cosθ-sinθ

A: In the question it is asked to calculate the area between curves r=2cosθ and r=cosθ-sinθ.

Q: Find the area in the first quadrant that is inside the circle r = 4 sin 0 and outside the lemniscate…

A: We need to find area.   NOTE - As per our guidelines we can solve one question so please upload…

Q: . The area of the region that lies inside the cardioid curve r = cos 0 + 1 and outside the circle r…

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Q: H.W: 1. Find the area of the region inside the oval limacon r = 4 +2 cos 0 2. Find the area of the…

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Q: Find the areas of the region shared by the circle r=2 and the cardioid r=2(1-cos 0). I r= 2(1-cos 0)

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Q: Find the area of the region inside the circle r = 18sinθ and outside the cardioid r = 6 + 6 sinθ.

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Q: Find the areas of the regions . 1.Inside the circle r = -2 cos u and outside the circle r = 1 2.…

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Q: Find the areas of the regions . 1. Inside one loop of the lemniscate r^2 = 4 sin 2u 2. Inside the…

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Q: Find the areas of the regions Shared by the circles r = 1 and r = 2 sin θ

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Q: Find the area of the region shared by the cardioids r= 12(1+ cos 0) and r= 12(1- cos 0). The area…

A: General equation of the cardioids is r=a(1+cosθ) and Area of the cardioids is 6πa2

Q: The area of the region inside the circle r= 6 cos e and outside the cardioid r= 2(1+ cos 6), a > 0…

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Q: 10. Find the area that's inside the curve: r = 3cos(0) but outside of r = 1 + cos(0). Draw

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Q: 6. Determine the area of the region (a) outside the cardioid r =1+ sin ở and inside the circle r = 3…

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Q: Find the area of the described region. region enclosed by one petal of  r = 6 cos(4?)

A: A=integration a to b 1/2r^2d(thita)

Q: Find the area of the region outside the cardioid r = 4 – 4 cos 0 and inside the circle r = 8. NOTE:…

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Q: The area of the region inside r = 6 cos 20 the rose and outside the circle = 3/2

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Q: 5. Find the area of the region contained inside the unit circle {x² +y? = 1} and outside the rose…

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Q: Find the area of the region that lies inside both curves r = 1 + cos(2theta) and r = 1

A: Here we have to find the area of the region that lies inside both curves r = 1 + cos(2θ) and r = 1…

Q: Find the area of the region common to the circles r= - 2 cos 0 and r= 1.

A: Given, r = -2cosθ, r=1point of intersection-2cosθ=1 ⇒cosθ=-12⇒θ=π-π3, π+π3    =2π3, 4π3

Q: Find the area inside of the cardioid r = 4(1 + cos(4)) and outside of the circle r cos(4). d) e) 49n…

A: Area under polar curve.

Q: - T If the area outside the cardioid r = 6 – 6 sin 0 and inside the circle r = 6 is A - , then what…

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Q: 7) Find the area of the region enclosed by the cardioidr = 4 cos 20.

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 6) Find the area of the region R that lies inside the circle r= 4(sin 0) and outside the cirele r –…

A: In this question we have to find Area of the Region that lies inside the circle.

Q: Find the areas of the region r = cos 30 O 3*pi/16 O pi/24 O 5*pi/14 O pi O 3pi/12 O pi/2 O other:

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Q: Find the area of the region outside the cardioid r = 4 – 4 cos 0 and inside the circle r = 11. NOTE:…

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Q: 1. Find the area common to both r=2 and r=4 cos 30 11A 6. Зх 101

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Q: Find the areas of the regions . 1Inside the circle r = 4 cos u and to the right of the vertical line…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 1. Find the area of the region inside the oval limacon r=4+2cos0 2. Find the area of the region…

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Q: Find the area of the region outside the cardioid r = 4 – 4 cos 0 and inside the circle r = 12. NOTE:…

A: Cardioid: r = 4 - 4 cos θ Circle: r = 12 Find the area of the shaded region.

Q: Find the area of the specified region. Shared SE by the circle r= 5 and the cardioid A) B) = 5(1+…

A: This problem is related to application of integration

Q: 7. Find the area of the shaded region. Give the exact value for the answer. V = = sec?x y = cos x 4

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Q: 10) Find the area of the region enclosed by the cardioid r = 12(cos 30).

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Q: Find the areas of the regions Inside the lemniscate r2 = 6 cos 2θ and outside the circle r = √3

A: Given that: r2=6cos2θ,     r=3 To calculate the points of intersection,   Set the given equation…

Q: The area of the region inside the rose r = 8 cos 20 and outside the circle r = 4/2

A: Given r=8cos2θr=42

Q: 3. Find the area of the region that lies inside the circle r = 1 and outside the cardioid r = 1- cos…

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Q: 3. Find the area of the region that lies inside the circle r - 1 and outside the cardioid r = 1 –…

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Q: 2. (a) Find the area of a region that lies inside the circle r = 2 sin 0 and outside the circler 1.

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Q: 7. Find the area of the region that lies inside both of the circles; [Ans: }( – 1)] r = 2 sin 0, r =…

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Q: (e) Find the area of the region inside the circle r = 3 sin and outside the cardioid r=1+ sin 0.

A: Above question is solved.

Q: 2. (a) Find the area of a region that lies inside the circle r 2 sin 0 and outside the circle r = 1.

A: As you post multiple questions According to the guideline I only solve the first problem please post…

Q: Find the area of the specified region. Shared by the circles r = 8 cos(e) and r = 8 sin(8) %3D A)…

A: Given :   r = 8 cos ( θ )   r = 8 sin (  θ )

Q: e the area of the region enclosed by r=√3 cosθ and r=sinθ on [π/3, 4π/3]

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Q: Find the area of the cardioid r = 2(1+ cos 0). Α. 2π В. 47 С. D. 67 E. none of the above

A: Given r= 2.(1+cos@) To find area of cardioid

Q: Find the area. a. Inside one leaf of the three-leaved rose = cos30 b. Shared by the circle r=2 and…

A: Given that a) r=cos(3theta) b) r=2 and r= 2 (1 +sin(theta)) c) r=-3cos and r=1-cos( theta) We have…

Q: Find the area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1 – cos 0). The area…

A: Given: r=12(1-cosθ) r=121+cosθ

Q: If the area enclosed by the curve x = 5 cos³ t and y = 5 sin° t (where t E R) is A, then what is A?…

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Q: Find the area of the specified region. 3 and the cardioid A) (6r + 8) 9. в) - (5я - 8) Shared by the…

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Q: 6. Determine the area of the region (a) outside the cardioid r =1+ sin ở and inside the circle r = 3…

A: Solution is provided here in the picture

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.