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

Q: Find the area of the region enclosed by one loop of the curve. r = 8 sin(5θ)

A: Our Aim is to find the area of the region bounded by one loop of the curve given by r=8 sin(5θ) -(i)

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 that is inside both r=1−sinθ and r=2+sinθ

A: Graph:

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

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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 the region enclosed by one loop of the curve. r = 8 sin(30)

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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 inside r=1+sin θ and outside r=3sin θ.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

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

A: Given r=cosθ for -π2≤θ≤π2

Q: 6) Find the area of the region R that lies inside the circle r= 4(sin 0) and outside the cirele r –…

A: In this question we have to find Area of the Region that lies inside the circle.

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: Find the area of the region outside 5+5 sin 0, but inside r 15 sin 0.

A: The area of the polar region: - The area of the polar region R is(r,θ): 0≤g(θ)≤r≤h(θ),α≤θ≤β where…

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 the region that lies inside r=3cos(theta) and outside r=1+cos(theta).

A: Given that two polar equation and find the area of using this inside r = 3cos( theta) and outside=…

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

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Q: Find the area pebal r=4 sin C30) of one

A: Let's now plot the graph:

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 enclosed by r = 2 sin 30.

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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: 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: 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 of the region enclosed by one loop of the curve. r = 4 sin(9θ)

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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 enclosed by r = 5 − sin(θ)

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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 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 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<=b<= 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.