of the negida cut from the first aree 2- Find the quadrant by the regiön r= I+Sin@ ?

Q: Find the area of the region enclosed by one loop of the curve  r= 3cos4(theta)

A:

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

A:

Q: Find the area of the region shared by the circle r=2 and the cardioid r=2(1-cos 0).

A: r=2 and r=21-cosθ Point of intersection 21-cosθ=21-cosθ=1cosθ=0θ=π2 So,  Area=Area of half…

Q: 1) Find area inside the circle r= 4cuse and to the right of line r = sece %3D

A:

Q: H.w. Find the areas for the hollawing regions: Region enclosed by the cardioid (r=\-sin@) in 1-st…

A: graph: r=1-sinθ

Q: Consider the quarter-circle of radius 1 and right triangles ABE and ACD given in the accompanying…

A: Here the objective is to prove the identity given below:

Q: How many square units is the area of the region enclosed by the polar curve r^2 = 4 cos 2@ ?

A: First we have to determine the limit of the function, then calculate it's integral

Q: Find the area of the region One petal of r = 2 cos 3

A:

Q: Find the area of the region One petal of r = 2 sin 6θ

A: Now the graph is,

Q: The area common to the circle > = 3 and the cardioid r = 3(1 - cos 9).

A:

Q: Find the areas of the regions Shared by the circle r = 2 and the cardioid r = 2(1 - cos θ)

A:

Q: Find the area of the region. Three petals of r = cos(50)

A: Find the area of the three petals of r = cos(5θ).

Q: Sketch the region that lies inside the circle r = 6 cos 0 and outside the circle r = 3. Th ind the…

A: Given region lies inside the circle  And outside the circle

Q: Find the area of the region              Shared by the circle r = 2 and the cardioid r = 2(1 - cos…

A: Given: The circle r = 2 and the cardioid r = 2(1 - cos u)

Q: Find the area shared by the circle r, = 9 and the cardioid r, = 9(1 - cos 0). .....

A:

Q: 3. Find the area of the region enclosed by one loop of the curve r = 4 cos 30.

A: Solution:Given  r=4 cos 3θTo find the area of the regionFormula:Area enclosed by one of the…

Q: 7) Find the area of the region enclosed by the cardioidr = 4 cos 20.

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the area of the region outside the cardioid r = 2 – 2 cos 0 and %3D inside the circler = 4.…

A:

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: Find the area of the region Shared by the circles r = 2 and the cardioid r = 2(1 - cos u)

A: r=2 and r=21-cosu Now, substitute 2 for r into equation of cardioid. 21-cosu=21-cosu=1cosu=0u=-π2…

Q: Find the area of the region                  Inside one loop of the lemniscate r^2 = 4 sin 2u

A: Given: r2= 4 sin 2u

Q: Find the areas of the region r = cos 30 O 3*pi/16 O pi/24 O 5*pi/14 O pi O 3pi/12 O pi/2 O other:

A:

Q: Find the area of the region common to the circles r=-6 sin 9 and r= 3.

A:

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 1 +…

A:

Q: Determine the area of the region enclosed by r=√3cosθ and r=sinθ on (π /3, 4π /3)

A: To find the area of the region enclosed by two polar curves, use the formula, A=∫αβ12r02-ri2dθ and…

Q: Find the area of the shaded region. r = sin(20) r = 4+3 cos (8)

A:

Q: Find the area of the region inside the circle r=-4cos(theta) and outside the circle r=2.

A: Given the region inside the circle r=-4cosθ and outside the circle r=2.   To determine the are of…

Q: 10) Find the area of the region enclosed by the cardioid r = 12(cos 30).

A:

Q: find the mside the r= 2a cos curve of region area the outside the r=Q arcle .

A: From given,we have to find the area of the region inside r=2a cos(theta) and outside r=a

Q: Find the area of the region enclosed by one loop of the curve. r = cos 48

A:

Q: 7. Find the area of the region cut from the first quadrant by the curve r = 2(2 sin 20)¹/2

A: Solution :

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 of the region that lies inside the cardoid r = 1 + cos 0, and outside the circle r =…

A: We have to use formula for area under a polar curve.

Q: Find the area of the region inside the circle r=-4sin(theta) and outside the circle r=2

A: Given, the area of the regionis inside the circle r=-4sinθand out side the circle r=2.

Q: Find the area of the region that is enclosed by the cardiod r = 6+ 6 sin 0. NOTE: Enter the exact…

A:

Q: Find the area of the shaded region. r = √cos 20 r = 5 cos 0 NOTE: Enter the exact answer. A

A:

Q: 2. (a) Find the area of a region that lies inside the circle r = 2 sin 0 and outside the circler 1.

A:

Q: Find the area of the region inside both the circle r=6 and the cardioid r=4+4cos(theta) (in other…

A: Given a circle and a cardiod in the polar form. We need to find the area inside the circle and…

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

A:

Q: Find the areas of the regions Inside the circle r = 3a cos θ and outside the cardioidr = a(1 + cos…

A: Given: The regions Inside the circle r = 3a cos θ and outside the cardioid r = a(1 + cos θ), a >…

Q: Draw a circle of radius 3.4cm. Draw one diameter of the circle. Shade one of the two semi- circular…

A: Given, We have to draw a circle of radius 3.4 cm. its one diameter and shade one of the two semi…

Q: Find the length of the entire perimeter of the region inside r = 6 sin 0 but outside r = 3.

A: Given the equation of the polar curve is, r=6sinθ Solving the equation r=6sinθ and r=3 for θ,…

Q: Find the area shared by the circle r,= 10 and the cardioid r, = 10(1- cos 0). %3D

A:

Q: Find the length of the entire perimeter of the region inside r = 6 sin 0 but outside r = 1.

A: Given that  r=6sintheta and r=1 To find the length of the entire perimeter of the region

Q: 2. Find the length of the entire perimeter of the region inside r = 14 sin 0 but outside r = %3D…

A:

Q: Find the exact area of the region, points and area of intersection inside r = 2 sinΘ and outside r =…

A: Firstly lets draw the graph of both the curves and find intersection area and intersection points.…

Q: Find the areas of the regions Inside the six-leaved rose r2 = 2 sin 3θ

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.