Calculate the area between the curves r2 16 sin 20 and p2 16 cos 20 .Show by drawing. %3D %3D

Q: Find the area inside the curve r = 6 cos 20 and outside the curve: r = V3

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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 of the shaded region. r=av cos 20

A: The given polar equation is: r=acos (2θ) The given region is from θ=-π4 to θ=π4

Q: Find the area of the shaded region in the following graph: y 2 y = sec? y = sin(4x) T/8 T/4

A: The figure is given by To evaluate : The area of the shaded region.

Q: Find the area of the shaded region. r = 6+5 cos

A: Introduction: The formula of the area inside the curve r=f(θ) is given by, A=∬rdrdθ Where limit of…

Q: Sketch the curve and find the area that the curve encloses. r = 3 cos 50

A: The solution for the above question is as shown below.

Q: Find the area a) Inside the lemniscate r = 6 cos 20 and outside the circle r = V3.

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: Find the area that the curve encloses and then sketch it. r= 10 cos(36e) y 5 -5 -5 - to -5

A: Answer

Q: Find the area of the region that is inside the circle r = sin θ and outside the cardioid r = 1 −cos…

A: Please see the below picture for detailed solution.

Q: Find the area between the innér and outer loops of the limaçon r = 2 – 4 sin .

A: This is a problem related to area of the polar curve. based on the graph of limacon curve we will…

Q: Find the area shared between the curves r = cos(θ) and r^2 = 3 cos(2θ)/2

A: First of all, we will plot the graph of the given curve and identify the shared region. The given…

Q: Find the area of the region inside one leaf of the three-leaved rose r=2 cos 30.

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Q: Find the area of the region enclosed by one loop of the curve. r = 5 cos(70)

A: To obtain the limits of integration, calculate the values of θ from the equation r=5cos7θ when r=0.…

Q: Find the area Inside the larger loop and outside the smaller loop of the limaçon r= + cos(@).

A: Sketch the graph of the limacon r=12+cosθ. We need to find the area of the shaded region.

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

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Q: Find the area that the curve encloses and then sketch it. r = 11(1 + cos ?)

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Q: Find the area inside the larger loop and outside the smaller loop of the limaA§on r = 1 + cos(0).

A: Given that: r=12+cosθ The area of the curves in the polar coordinate is given by the formula,…

Q: Find the area in the second quadrant enclosed by r = 2+2 cos 0.

A: Consider the given equation, r=2+2cosθ In the given graph, the angle θ is lying 0 to 2π. The area…

Q: Find the area of the region that Iies inside both curves. -V 3 cos(@), r= sin(8)

A: Finding point of intersection Set up integral as A=∫αβ(rθ)2dθ

Q: Find the area inside both curves in Figure 23. r=2+ sin 20 r=2+ cos 20 FIGURE 23

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Q: (b) Sketch and find the area of the region enclosed by the curve r = 4 cos 30

A: b) Given region is r=4cos3θ. Sketch the graph of the region as shown below.

Q: Find the area closed by the astroid ,3 x = a cosº 0, y = a sin³

A: Here we have to find the area closed by the astroid,  x=acos3θ, y=asin3θ

Q: Find the area of the region inside one leaf of the three​-leaved rose r=cos3θ.

A: Area of the one leaf = 1l2∫r² dθ

Q: Sketch the region and find the area it enclosed r = 3(1+ cos 0)

A: The area, A of the polar curve r=fθ in the interval a, b is calculated using the formula: A=∫ab12r2…

Q: b) Inner loop of r = 8 – 16 sin (e)

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Q: Find the area of the following shaded region. y = 1 y = cosx

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Q: Find the area of the region bounded by: r 50 cos 28

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Q: 4. Find the area that lies inside the curve r = 4 cos and outside the curve r = 2.

A: Given, curves are

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 10…

A: The required region is as follows.

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: Find the area of the region enclosed by one loop of the curve. r2 = 4 cos 20

A: The curve is r2=4cos2θ. Rewrite r2=4cos2θ as r=4cos2θ . When θ=0, r=±2 and θ=π4, r=0 Sketch the…

Q: Find the area of the shaded region in the diagram given below. y = sin(2r) 6 y = cos(x)

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Q: Find the area of the region bounded by: r 98 cos 20

A: Solving

Q: Find the area of the region bounded by: 6 cos(20) 0 < 0 < 2m

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Q: Find the area enclosed by the curve r2 = a² cos 0 (2 – cos? 0)

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Q: Find the area of the shaded region shown in the graph. Ay y = 27 sin x 27 y= 27 cos x

A: Solution :-

Q: r = 3 cos 0

A: The given curve,  r=3 cosθ

Q: Find the exact area of the region inside r = 2 sinΘ and outside r = sinΘ + cosΘ.

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Q: Find the area of the region that lies inside the first curve and outside the second curve. r= 14 cos…

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Q: Find the area of the area inside the curve) r = a (1 + Sin0 and outside the circle r = aSin0.

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Q: Q2: Find the area common between the curves r = a (1+ cos0), r =a (1 – cos0).

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Q: Find the area of the region inside one leaf of the three-leaved rose r= 4 cos 30.

A:

Q: Find the area of the region enclosed by one loop of the curve. r=3cos(θ)

A: Kindly follow the attached image.

Q: Find the area between the two curves in the following figure: r=2a+acos 20 r =sin 20 For a = 14

A: Given: r=2a+acos2θr=sin2θa=14

Q: . Find the area between the curves r = sin0, and r = V3cos0

A: Area of polar curve

Q: Find the area of the region that lies inside both curves. r = (3)1/2 cos(θ),    r = sin(θ)

A: Calculate the value for intersection points and the values for theta where both the value for both…

Q: Find the area enclosed by the curve r“ = a“ cos e (2 cosʻ 0) -

A: Given:

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.