Find the area enclosed by the curve: r = 4 +2 cos 0

Q: Find the area of the region Inside the cardioid r = a(1 + cos u), a > 0

A: Given  r=a1+cosu, a>0

Q: Find the area of the region that lies inside both curves. r=6+cos(theta) r=6-cos(theta)

A: Here we will find out the required area

Q: Find the area inside the cardioid r = 4 + sin∅ from ∅=0 to ∅= 2π.

A: The area inside the cardioid rθ is found out using the formula: A=12∫abrϕ2dϕ , a≤ϕ≤b Now, we have…

Q: 2y? and x = 4 + y²

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Q: Find the area enclosed by the cardioid r = a(1 + cos θ), where a > 0.

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Q: Find the area of the region bounded below by the x-axis and above by the curve T æ = 2 sin?(0), y =…

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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 of the region enclosed by one loop of the curve. r = sin(120)

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Q: Find the area enclosed by the following curves: d). r = 2 cos 20

A: Given   r=2cos2θ

Q: Find the area of the region thatlies inside the cardioid r = 1 + cos θand outside the circler = 1.

A:

Q: Sketch the region enclosed by the given curves and find its area. y= cosx, y= (1-2x)/pi

A: y=cosx  &  y=1-2xπ The region enclosed by these curves is,

Q: Find the area enclosed between the curve y = cos? x and the line y = 1: %3D Y= cosr

A: Here we have to find the area of the bounded region between the curve y=cos2x and the line y=1

Q: Find the area under one arch of the cycloid x = a(t - sin t), y = a(1 - cos t).

A:

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

A: first we need to find  the 9cosθ=4+cosθ that gives cosθ=1/2=θ=±π3 the area is given by

Q: Consider the curve r = √[1+sin(θ)], where 0 ≤ θ ≤ 2π. (a) Compute the area enclosed by the graph of…

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Q: Find the area enclosed by the curve r = v6(1 – sin®).

A: Area of Polar curve is given by:

Q: Find the area bounded by the curve r2 8 cos 0. %3D

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Q: Find the area enclosed by the astroid x = cos3 t, y = sin3 t, 0 ≤ t ≤ 2π.

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Q: Find the area enclosed by the curves y = sin x y = cos x from x = 0 to x = T. and

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Q: Find the area bounded by the curve x=3+cosØ, y=sinØ

A: the given curves are x=3+cosϕy=sinϕ

Q: Find the area bounded by the curve x = 3+ cos Ø, y = sin Ø.

A: The solution is given below

Q: Find the area enclosed by the curve r V6(1 – sin®). %3D

A: First we will plot the curve and and using Double integration we will find area bounded

Q: Find the area of the region enclosed by the curves: y = e2", y = et", æ = 1

A:

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 between y = vx and y = Vx +1, with 0 < x< 4. Sketch the region.

A: find the area between y=x and y=x+1 , 0≤x≤4

Q: The area enclosed by the curve r = 3cos30 is

A: Given curve is that, r = 3cos3θ we have to find the area bounded by given curve.

Q: Find the area bounded by the curve r= 2+cos θ

A: Given problem:- Find the area bounded by the curve r= 2+cos θ

Q: Find the area of the region that lies inside both curves. r = 1 + cos 0 аnd r = 1 – cos 0

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Q: Find the area of the region bounded by the curve r = 8 cos 2θ.

A: We need to find the area of the region bounded by the curve r = 8 cos 2θ. Let us first plot the…

Q: r =1- cos 0 r=1+cos 0

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Q: The area enclosed by the curve r = 3cos30 is of

A: The graph of the given polar equation

Q: Find the area of the region that lies inside the cardioid r = 1 + cos u and outside the circle r =…

A: We first find where they meet

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

A: The formula for the area between two parametric curves is given by

Q: Sketch the area enclosed by the curves and find its area. y=cos2x y=0 x=pi/4 ×=pi/2

A: Given,

Q: TT 8. Find the area between the curves y = cos r and y = sin x, %3D

A: Between pi/4 to pi/2 sinx is greater than cosx  So y=sinx will be above y=cosx between pi/4 to pi/2…

Q: Find the area of the region that lies inside both curves. r = 2 + cos(0), r= 2 – cos(0)

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Q: Find the area of the shaded region 14 LA bounded above by y = 2, bounded b TE lo 1)

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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: 30. r = 1 + cos 0, r =1 – cos 0

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Q: Find the area of the region that lies inside the first curve and dutslde uie 18 cos(20), r= 3

A: Given: First curve is r2=18cos2θ Second curve is r=3. Determine the intersection points by…

Q: Find the area enclosed in a curve r=24cos20.

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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 enclosed by the curve r=2cos angle

A: Given:       r=2cosθ Area of polar region A=12∫αβr2dθ

Q: Find the area obtain when the curve f(x) = x² - In r, for 1 <a< 3, is rotated about the y-axis.

A: The area obtained when the f(x) is rotated about the y-axis is given as: where a is the lower limit…

Q: r = 3 cos 0

A: The given curve,  r=3 cosθ

Q: find the area of the surface formed by revolving the cardioid r= a(1+cosθ) about the x-axis

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Q: Find the area of the region that lies under the curve v = sin r on the interval 0 <r<"

A: