Find the area between the curve r = sin (3θ) and the first and second quadrant.  Graph.

Q: A. Find the area enclosed by each of the following curves. T= 4 sin e

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Q: Find the area between the two curves in the following figure: r=2a+a cos 20 r=sin 26 For a = 16…

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Q: Find the area: y = sin x, the x-axis, the y-axis and the vertical line x = 2 *

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Q: Find the area of the region Inside one leaf of the four-leaved rose r = cos 2u

A: Given:  r = cos 2u

Q: Find the area of the region cut from the first quadrant by the cardioid r = 1 + sin theda.

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Q: r = 4 +3 sin 0

A: Consider the curve  r=4+3sinθ

Q: Find the area enclosed by the curve p? = 3 cos(50) %3D

A: Plot the graph of the given polar equation

Q: Find the area bounded by the parabola x² = - (y - 1) and the first quadrant.

A: Intersection points:y=0x2=1;x=1 (First quadrant)(1, 0)x=0:1-y=0y=1(0, 1)

Q: Find the area in the first quadrant that lies within the curve r 1+ cose.

A: Here,  r = 1+ cos(theta) We know that,  Area = 1/2  {integral of r2 w.r.t theta}

Q: Find the area of the region inside the circle r = 4 cos θ and outside the circle r = 2.

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Q: TT he area of the region between the sine curve and the x-axis from 2

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Q: Compute the exact area that is inside the circle (r = 14) and outside the petal of the flowered…

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Q: Find the area of the shaded region. =3 sece tan e

A: To find the area of the shaded region

Q: What is the area between the curve G(b) = 3 sin(b) and the horizontal axis, between the points b…

A: (a) Given curve, And the horizontal axis between the points  To find: Area under the curve G(b) on…

Q: Find the area of the region. Interior of r = 6 sin e

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Q: Find the area. Sin 9in BD = 6in B. A,

A: Use formula of area of triangle

Q: Find the area of the region. Interior of r = 8 sin e

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Q: Find the area of the shaded region. r= 4 + 3 sin e

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Q: egi =y=sin{x} eq2 =y=cos( 3 2.

A: Given equations are y=sinx and y=cosx. To find: Area using horizontal strips.  Differentiation…

Q: Find the area of the shaded region. r= 4+3 sin 0

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Q: Find the area of the region inside the circle r=2 COS e ɑnd outside the circle r= |

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Q: Find the area of the shaded region. r = sin(20) r = 4+3 cos (8)

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Q: graph. Find the area common to the circle r = 3 and the cardioid r = 3(1 – cos 0).

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Q: 28. y A y = sin x 1 TT y = sin 2x

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Q: Find the area of the region inside 2 petals of the rose r = sin 80

A: Solution :-

Q: Find the area in the sec ond quadrant under 1 the curve x´y = e*. A =1 sq. units

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Q: r = 4 sin 0

A: Given Polar equation is r = 4 sin θ Find the area of the enclosed by the given curve  Area under the…

Q: Bm 11 2元

A: we need to find the integral of the function in the given limits to get the

Q: a- Graph r=3 sin 20 b- Evaluate the area inside the curve

A: We have to evelaute the area inside the curve r=3sin2θ.

Q: Find the area of the shaded region. r = 1 + cos 0

A: Here, the given curves are r=1+cos θ & r=3 cos θ First of all find the intersection points of…

Q: Find the area of the region enclosed by one loop of the curve. r = sin(80)

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Q: What is the area of the shaded region? y = sin x TT ST 6

A: From the given region; So, The point of intersection between the curve and line is:…

Q: Find the area of the shaded region shown in the graph. y = 12 sin x y= 12 cos x .

A: Given, The two curves y=12sinx and y=12cosx intersect atx=π2 in x∈(0,π)

Q: find the area of the circle r=a by integration

A: The diagrammatic representation is,

Q: Find the area of the region inside the circle r= 32 cos 0 and to the right of the vertical line r= 8…

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Q: Find the area of the region inside: r = 7 sin 0 but outside: r = 1

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Q: Find the area of the specified region. Inside the -6 sin(0) and outside the circle circle r = A) B)…

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Q: The area enclosed by the circler= = sin 0 is given by 2x esin 0 A = f" Sr dr d0.

A: Given that  The area enclosed by the circle r=sintheta is given

Q: Find the area of the region inside: r 8 sin 0 but outside: r = 1

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Q: find the area enclosed by r = 5 − sin(θ)

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Q: r=2a+acos 20 A r=sin 20

A: The polar curves do not intersect at any point. The area between the curves is the shaded region.

Q: Find the area of the shaded region in the following figure y = sin x 5п

A: Find the functions f (x) and g (x).

Q: ind c such that the area between the curves y = r- c and y = c -2 is equal to 69. Round your nswer…

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Q: 14. Find the area of the curve p2 r² = 16 cos 20

A: Find the area of the given curve

Q: Find the area of the region enclosed by one loop of the curve. r = 4 sin(70)

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Q: Find the area of the specified region. Inside the circle r=6 and to the right of the line r= 3 sec 0

A: Given problem is :

Q: T= 8 cos 30. with /met: A =

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Q: Find the area of the region inside: r = 7 sin 0 but outside: r = 3

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 inside: r 10 sin 0 but outside: r = 1

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.