Evaluate ldAwhere R is the region in the first quadrant that is outside the circle 1=l and inside the cardioids r=1+cos 6.

Q: Find the area of the region shared by the cardiods r=12(1+cosθ) and r=12(1-cosθ)

A:

Q: Find the area of the region shared by the cardioids r= 9(1 + cos 0) and r=9(1- cos 0)

A:

Q: 2. Find the area of the region R that lies inside the cardioid r= (1+ cos0) and outside the circle…

A:

Q: Graph the cardioid r = a(1+ sin®), a< 0?

A: We are given that r=a(1+sin∅), a&lt;0 Here as we know that sin∅ is always greater than equal to -1.…

Q: Find the area of the region common to the circles r= - 2 cos 0 and r= 1.

A: Given, r = -2cosθ, r=1point of intersection-2cosθ=1 ⇒cosθ=-12⇒θ=π-π3, π+π3    =2π3, 4π3

Q: Find the area inside the large loop and outside the small loop of r = 1 + 5 sin(θ)

A: Given, r=1+5sinθ Firstly, sketch the graph of the region to find the area.

Q: B-Find the area of the region inside the carver-1+cose and outside the curve -1 and graph the two…

A:

Q: 3. Find the area of the cardioids region shared by ri 7(1- sin 0) and r2 = 7(1+sin 0). A 7(1 Sint) B…

A: The given curves are:  r1=71-sinθr2=71+sinθ To find the intersecting points,…

Q: Find the area of the region of intersection of the curves r = 4+3 cos 0 and r = 2 cos 0. Identify…

A: The given curves are r=4+3cosθ and r=2-cosθ. To Find: (i) The area of the region of intersection of…

Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: The area in the black color is r = cos e

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.