Find the area of the specified region. Inside the outer loop and outside the inner 6 cos(0) – 3 A) 9(7 +3/3) B) (2 - 3/3) loop of the limacon r = 3 (4т + 3/3) D) (47 – 3/3)

Q: 2. Find the area of the region inside the cardioids r= a(1+ cos 0), a>0

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Q: Find the area of the region bounded by: r = 7 cos(100) 0 < 0 < 2n

A: The formula for area is - A=12∫abr2dθ

Q: Find the area inside the smaller loop of the limaçon r= 2 cos 0+ 1.

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Q: 2. Find the area of the region R that lies inside the cardioid r= (1+ cos0) and outside the circle…

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Q: 1- Find the area of the region enclosed by the cardioid r =1+ cos 0

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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 given region analytically. between the loops of  r = 4 − 8 cos(?)

A: First find the limit for the integral used to find the area:   Find the limit of the function:…

Q: Find the area of the specified region. 9) Inside the outer loop and outside the inner loop of the…

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Q: A. Determine the area inside the smaller loop of the limaçon r = 1-2 sin 0 exactly. 12

A: Area can be found by using definite integration.

Q: Find the area inside one leaf of the three-leaved rose r = cos(30), as scen here: -0.4 -0.2 0.2 0.4…

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Q: Find the area of the region              Shared by the circle r = 2 and the cardioid r = 2(1 - cos…

A: Given: The circle r = 2 and the cardioid r = 2(1 - cos u)

Q: Find the area of the upper half of the graph r = 1 - cos(2θ)

A: First, find the angle when the polar curve intersects x-axis, 0=1-cos2θcos2θ=1cos2θ=cos0,cos2πθ=0,π

Q: 4. Find the area common to the circler=3 cos 0 and the cardiod r=1+ cos0.

A: Find points of intersection and solve the given problem. A detailed solution is given below.

Q: Find the area of the region. (c) Between the loops of r =1+2 cos 0

A: Solution is given as below:

Q: (ii) Find the area of the region bounded by r - 200 cos (20).

A: To find- Find the area the region bounded by r2 = 200 cos2θ.

Q: B. Find the area of the region bounded by the following: 18. common to 7 = 3 cos and r=1+ cos

A: 18. The given curves are r=3cosθ and r=1+cosθ. To find: The area under the curves . Please post the…

Q: 3. Find the area of the region enclosed by one loop of the curve r = 4 cos 30.

A: Solution:Given  r=4 cos 3θTo find the area of the regionFormula:Area enclosed by one of the…

Q: Q5 Find the area of region enclosed by the r=1-e cos 0

A: We know that  the area of a sector of a circle is 12α r 2 , where α is the angle subtended by the…

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: Find the area of the region Shared by the circles r = 2 and the cardioid r = 2(1 - cos u)

A: r=2 and r=21-cosu Now, substitute 2 for r into equation of cardioid. 21-cosu=21-cosu=1cosu=0u=-π2…

Q: Find the area of the region bounded by: r : 6 cos(40) 0 <0 < 2n %3D

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Q: B. Find the area of the region bounded by the following: ²= 2 cos 20 and outside r = 1 20. inside

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Q: Find the area of the region shared by the cardioids r= 8(1 + cos 0) and r= 8(1 - cos 0).

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Q: Find the area between the loops of the limacon r = 7(1+ 2 cos 0). Area =

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Q: B. Find the area of the region bounded by the following: 18. common to r = 3 cos 0 and 1=1+cos (

A: We have to find the area of the region bounded by r=cosθ and r=1+cosθ

Q: 5) Find the area of the region R that lies inside the cardioid r= 2(1+ cos 0) and outside the…

A: To find the area of region R that lies inside the cardioid r=2(1+cos θ) and outside the circle r=3.

Q: Find the area of the specified region. Inside the graph of r = 4 + cos(30)

A:

Q: 4) Find the area of the region R that lies inside the cardioid r=(1+cos 0 ) and outside the…

A: We have to find area of the region R that lies inside the cardioid , r=(1+cosθ) and outside the…

Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

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Q: Find the area of the shaded region

A: Required area is,

Q: 9) Find the area of the region common to the r= (1+ cos 0) and r = (1- cos 0 ).

A: For the given problem Diagram is given as follows:

Q: 2. Find the area enclosed by T = @ cos 30-

A: We need to find area.

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: Find the area of the region bounded by: r 9 cos(80) 0 < 0 < 2T

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Q: Look for the smaller loop of the limacon r = a(1+2 cos 0) and solve for its area.

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Q: Find the area of the region enclosed by one loop of the curve. r = cos 48

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Q: Find the area of the region bounded by: r = 10 cos(100) 0 <0 < 2n

A: Given :r=10cos(10θ) 0≤θ≤2πTo find : The area of the region

Q: Find the area of the region shared by r =1+ cos 0 and r =1– cos 0.

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Q: The area of the region in the first quadrant that is within the cardioid r = 1 - cos0 is

A: Givne that  r=1-costheata To find teh area of the region

Q: Find the area between the loops of the limacon r = Area = 5(1 + 2 cos 0).

A: We have to find the area between the loops.

Q: Find the area of the region shared by r=1+ cos 0 and r =1– cos 0.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

A:

Q: B. Find the area of the region bounded by the following: 18. common to r=3 cos 0 and *=1+cos 0

A: Given that r=3cosθ, r=1+cosθ

Q: Let R be the region bounded by the inner loop of the limacon, r = 4V3 shown in the diagram below.…

A: Integration of function equation under certain limits give the value of area under the function…

Q: 1. Find the area of the region outside r = 2/3 + cos 0 and inside r = 5 cos 0.

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Q: Find the area of the green shaded of the region where r = - cos(20) and r = - cos(0) as shown in…

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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: Given: r=12(1-cosθ) r=121+cosθ

Q: 5) Find the area enclosed by the circle r = 3 cos 0 and the cardioid r =1 + cos 0.

A:

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

Q: 17. Find the area of the region that lies inside the first curve and outside the second curve. r = 2…

A:

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.