Find the area of the region R inside the curve r= 9sine and outside the curve r=3+3sine. V3 9π+ 4 A V3 9π- 4 c) (D) 18T

Q: 5. Find the area of the region that lies inside the curve r =1+ sin 0 and inside the curver = 1.

A: The given data is: r=1+sinθ      ........1r=1                .....2 To find the area of the region…

Q: Q45.a) Find the area of the region enclosed between the curves y= cos(2x), y=0, x=r/4, x- 1/2…

A: Make the graph and than use the integration to find the area.

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: Q41.a) determine the area of the region bounded by x=-y2-3 and x= (y-2)2? (Sketch the region) Sany…

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Q: Please solve 18 and also answer the question of what fraction of the unit circle is contained within…

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Q: Q1/ / 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 that lies inside the first curve and outside the second curve. r = 6 −…

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Q: Find the area of the region that lies inside both the curves r = sin(0) and r= cos(0). A. (M В. (п…

A: This is a problem of integration. We will calculate the area by using integral method. Please follow…

Q: The area of the region outside the curve 1-2+2sin0 and inside the curve r-6sin0 is given by which…

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Q: Find the area of the region enclosed r = 2+ 6 cos 0 form 0 = 0 to 0 = ; %3D

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Q: Q45.a) Find the area of the region enclosed between the curves y= cos(2x), y=0, x=r/4, x= 1/2…

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Q: Q45.a) Find the area of the region enclosed between the curves y3 cos(2x), y=0, x=n/4, x3 n/2…

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Q: j: The area of the region that is inside of the cardioid r=2+2 cos 0 and outside of the circle r= 3…

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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: 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 that is bounded by the given curve and lies in the specified sector.…

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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: Find the area of the shaded region. r = V cos20 r = 6 cos 0 NOTE: Enter the exact answer. A

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

A: We have to find the area of the region that lies inside the first curve and outside the second…

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 that lies inside both curves. r = 4 + cos(θ),    r = 4 − cos(θ)

A: First of all, consider the polar equation of the two circles. Equate the two equations of the…

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

A: Let's find.

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 6 - 6…

A: The given region is r=6-6sinθ, r=6.

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: Find the area of ​​the area inside the curve r = 6 cos θ but outside the curve r = 2 + 2 cos θ.

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Q: Q2. Find the area of the region lies inside both curves (intercept area) (r1 cos0) and (r2 sine).…

A: Given that,

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: Q3. Find the area of the region R that lies outside the cardioid r = and inside the circle r a(1+…

A: q-3 find the area of the region R that lies outside the cardioid r=a1+cosθ and inside the circle…

Q: Find the area, A, of the region enclosed by the cardioid r = 10 + 10 cos 0. NOTE: Enter the exact…

A: solution given below

Q: Find the area of the region that lies inside the first curve and outside the second curve. r= 15 cos…

A: Given

Q: 2. Find the centroid of the area in the first quadrant under the curve y = 4 – x2. Answer:

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Q: A B D Find the area, A, of the region enclosed by the cardioid r = 8 + 8 cos 0. 96 л 52 t 48 100 π

A: First I have written the area formula for polar curve , then draw the graph of given curve and then…

Q: 23. r= 4 sin 0, r= 2

A: We have to find the area of the region that lies inside r=4sinθ and outside r=2

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r…

A: Given, r= 6 cos(θ) , 0 ≤ θ ≤ π/6

Q: Find the area of the shaded region. r = V cos 20 r = 9 cos 0 NOTE: Enter the exact answer. A =

A: We have to find the area under the curves r=cos 2θ and r=9 cosθ

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: Q9.a) Find the area of the region bounded by x = -Vy, and y = 4 (Sketch the region) %3D b) Solve to…

A: Sketch the given region        As per our guidelines we are supposed to answer only first question…

Q: Use Green’s Theorem to evaluate around the boundary curve C of the region R, where R is the triangle…

A: By Green's theorem, ∫CPdx+Qdy=∬DQx-PydA. Here the integral is  ∫Csin 5y dx+5y dy and the region is…

Q: Find the area of the region that lies inside the cardioid r=1+sin(θ) and outside the circle r=1.

A: Here we will use the following formula for calculating the area of the region R bounded by above…

Q: Q2) find the area of region in second quadrant within cardioid r = 1-cos0

A: We have to find the area of cardioid in second quadrant

Q: Consider the region bounded by the curves y = 0, r = -1, r = 1, and 1 (r² + 1)3/2" Find the area A…

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Q: (c) Find the area of the region common to the interiors of the cardioids T = 1+'cos 0 and r = 1- cos…

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Q: Find the area, A, of the region enclosed by the cardioid r = 6 + 6 cos 0. NOTE: Enter the exact…

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Q: Find the area of the surface generated by -y + e revolving the curve x = 2 Osys In 7 about the…

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Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 4 − 4…

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Q: Find the area of the region R inside the curve r= 6sine and outside the curve r=2+ 2sine. 4TT V3 4TT…

A: This question is related to integral calculus

Q: The area of the surface generated by revolving the line x = y from x= 0 to x=2 about the y-axis:…

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Q: Find the area of the region R inside the curve r=6sine and outside the curve r=2+2 sine. V3 4TT - B…

A: First, we have to sketch the curves, then identify the area required and then use the expression of…

Q: Determine the area of the region indicated in each exercise. Inside the circler=V3 sin 0 and outside…

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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.