Q2-)A-) Find the area lies inside of r = 1 + sin0 and outside r = 2sin0

Q: Find the area between the two Curv G. ye- -X, x² = G - Sy

A: Given that  y^2=-x,x^2=6-5y To find the area between the curves

Q: Find the area enclosed by the loop r = 2 cos 0 -- sec 0.

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Q: Find the area bounded by the ff. curves and lines: a. arch of y =(1/3)sin(x/3)

A: Consider  the equation

Q: Compute the area that is inside r = 3 + 3 sin and outside r = 2.

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Q: Let R be the region bounded by y 8 sin 2 point (? 8)

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find the area of the specified region. 5) Inside the limacon r= 8 + 2 sin 0

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Q: Determine the area that lies inside r = 3+2 sin 0 and outside r = 2. r-3+ 2sin e 2. B.

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Q: Find the area bounded by the curve r = 2 - cos 0.

A: The equation of curve is given as , r=2-cosθ Find the area bounded by the curve.

Q: Find the area that is shared by both cardioids r = 1 - cos(theta) and r = 1 + cos(theta).

A: Consider the region that is shared by both cardioids r = 1 - cos(theta) and r = 1 + cos(theta):

Q: Find the area of Sin(x) over the interval of (0, pi)

A: Area of Sin(x) over the interval of (0, pi) is given by:

Q: Find the area of the shaded region. 21) 2- y = 2 2 sin(my

A: Since we are given with the multiple number of question and answered according to the guideline

Q: Find the area bounded by the FF. Curved and lines a.) An arch of y= (1/4)sin(x/4)

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Q: 4. Sketch the region enclosed by y = 2x – x? and y = 0. Use calculus to find the exact area of this…

A: The solution is given below:

Q: Find the area bounded by the curve r = 2-cos 8.

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Q: Find the area bounded by r = cos 0 for -π/2 ≤0 ≤π/2.

A: Given r=cosθ for -π2≤θ≤π2

Q: Determine the area that lies inside r = 3+2 sin 0 and outside r = 2 r = 3+ 2 sin e -4 -3 8 = 4. r =…

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Q: Find the area in which region lies in first quadrant bounded by v = ³√(u) , u-axis and line v = u -…

A: In this scenario, there is a curve and a straight line. First we need to find the intersection…

Q: TT Find the area that is bounded by r = sin 0 and lies in 2 3

A: Given Data The equation of a curve is r=sin θ The interval of θ is π/2≤ θ ≤ 2π/3   The expression…

Q: 6) Find the area of the region that lies inside the curve r = 3sin0 but outside the curve r = 2 -…

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Q: Find the area under one arch of the trochoid и — 60 — 4 sin(0), у — 6 — 4 сos(0). - - Area =

A: To find the area under one arch of the trochoid. x=6θ−4sinθy=6−4cosθ

Q: 2- Region enclosed by the cardiaid (r=\- Sin@)in 1-st quadrant.

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Q: Find the area enclosed by the curve r = a(1 - sin theta).  Show full solution

A: We have to solve the problem

Q: the Area that lies inside r=3+2 sin 0 out side r=2 is 24.315 O -24.187 O 23.957 O 24.187 O -23.957

A: Solution:-

Q: find the area of r=9cos(theta) bounded by 0 ≤ θ ≤ π/6

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Q: Graph and Find the area of the region(s) enclosed by y 1+ sin x, y = 1- sinx, and -x

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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: Calculate the area between the curves r2=16 sin 2Ɵ and r2=16 cos 2Ɵ.show by drawing.

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Q: Find the area under the curve 3 over the interval [3, 8]. y = (4x + 2)² Enter the exact answer. area…

A: y = 34x+22,interval : 3, 8

Q: Find the area enclosed by r = 2 sin 30.

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Q: Find the area between y = 7 sin (x) and y = 7 cos (x) over the interval [0, π]. (Use decimal…

A: For the cartesian curves y1=f1(x) and y2=f2(x) where y2>y1 in the limit x=a to x=b, the area…

Q: Determine the area of the region (a) outside the cardioid r = 1+sin 0 and inside the circle r = 3…

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Q: Find the area in which region lies in first quadrant bounded by v=∛u ,u-axis and line v=u-n. Where…

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Q: Sketch the graph r=1- cos 0 and find the area enclosed by r=1- cos 0. استعراض جهاز الكومبیوتر إرفاق…

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Q: Find the area of the region enclosed by the astroid x=a cos3 θ,y=a sin3 θ. (Astroids are explored in…

A: To find the area enclosed by the asteroid x=acos3θ ,y=asin3θ

Q: Find the area between z%3D0 and z= 1

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Q: of one loop of the curve r = cos? 0 - sin? 0

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Q: find the area bounded by r = 9 + 2 cos(θ)

A: Here given the equation of cardioid as Then the area inside the cardioid is defined as

Q: the Area that lies inside r=3+2 sin 0 out side r=2 is -23.957 O -24.187 O 23.957 O 24.315 O 24.187 O…

A: We have r=3+2sinθ  , r=2 We find the point of intersection: 3+2sinθ=2⇒sinθ=-12⇒θ=sin-1-12⇒θ=7π6,…

Q: Find the area enclosed by r² = 4 sin 20.

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Q: Find the area enclosed by the curve r = 1 sin(0). Area =

A: The graph of the given curve is:

Q: e the area of the region enclosed by r=√3 cosθ and r=sinθ on [π/3, 4π/3]

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Q: Find the area between the graphs x = sin (9y) and x = 1 – cos (9y) over the interval 0 < y < in the…

A: Here we will find the area,

Q: Find the area bounded by the circle r = 2 sin 8 and r = 4 sin 0.

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Q: Find the area bounded by r2 81 cos 20. %3D

A: Let's find.

Q: Find the area that the curve encloses and then sketch it. r-1+6 sin(60) -6 -4 2 4 -6 ****

A: Given polar curve isr=1+6sin6θThe area enclosed by the curve is determined as shown below.The polar…

Q: Find the area in which region lies in first quadrant bounded by v=∛u ,u-axis and line v=u-n. Where…

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Q: Find the area enclosed by the curve r 1 sin(0). Area =

A: As per our guidelines only one question can be solved. Please find the solution of first question in…

Q: Find the area of the following: 1.y = COS X cos x and y = sinx [0,21]. on

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the exact area under the cosine curve y = cos x  from x =0 to x=b , where 0&lt;=b&lt;= pie /2.…

A: Giveny=cosx where x=0 to x=b                        and 0≤b≤π2.To find Area of cos x   where x=0 to…

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.