6. Determine the area of the region (a) outside the cardioid r =1+ sin ở and inside the circle r = 3 sin e. (b) between the loops of the limaçonr=÷+ cos e

Q: 18. Sketch the region that is inside the circle r = 3cos 0 and outside the cardioid r = 1 + sin 0,…

A: Sketch the graph. we need to determine the intersections of these curves as the limits for…

Q: Given an area D bounded by a cardioid r = 1 + cos θ, θ ∈ [0, π], x-axis, and it’s located on the…

A: If the curve is given by , where   .The area inside the  curve is  .

Q: 4. Sketch the curve of r2 = cos 20 and find the area that encloses it. Show your complete %3D…

A: Converting polar coordinates to rectangular coordinates  Put r=x2+y2,  θ=tan-1yx in r2=cos2θ…

Q: 6. Determine the area of the region (a) outside the cardioid r = 1 + sin 0 and inside the circle r =…

A:

Q: Find the area of the specified region. Inside the limaçonr=8+2 sin 0

A:

Q: 2. FIND THE AREA BOUNIDE O BY 2 y= x (2,4) and the X- axis THE CURVE

A: The given curve is: y=x2      .........(1)We have to find the area bounded by the curve y=x2, (2,4)…

Q: Find the area inside the smaller loop of the limaçon r= 2 cos 0+ 1.

A:

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

A:

Q: 9. Find the area of the region that lies inside both curves * r = 2 sin(0) and r = 2 cos(0) O -1 27…

A:

Q: e area between the two loops of the limacon r = 1+2 sin 0.

A: We are asked to find the area between the loops.

Q: 2. Find the area of the region that lies inside both curves r = 4 sin(0) and r = 4 cos(0) ● 플 +1 2T…

A:

Q: 2. Find the area of the region that lies inside both curves * r = 4 sin(0) %3D and r = 4 cos(0) 2л -…

A:

Q: .: The area of the region that is inside of the cardioid r = 2 +2 cos 0 and outside of the circle r=…

A: Area in polar form given below

Q: 1. Find the area of the region that lies inside the cardioid T-1+ sin 0 and outside the circle r -…

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: 4. Find the area between y sin(r) and y cos (2r) on

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: 1) Find the area a) Inside the cardioid r= 2 cos (0/3) and outside the circle of radius r = v2…

A: q-1(a) find the area inside the cardioid r=2cosθ3 and outside the circle of radius r=2 centered at…

Q: 4. a) calculate the area of the area bounded by the Curves TI y=Sin 2x and y sin 2x, OSX<

A:

Q: 5. Find the area of the region R that lies outside the curver=2 and inside the curve r = 4 sin 0

A:

Q: Find the area of the region enclosed between y= 3*sin(x) and y=4*cos(x) from x=0 to x=.6*pi

A:

Q: Find the area between the loops of the limacon r = 7(1+ 2 cos 0). Area =

A:

Q: 20 B-Find the area of the region inside the curve r-1+cose and outside the curve -1 and graph the…

A:

Q: 5) Find the area of the region R that lies inside the cardioid r= 2(1+ cos 0) and outside the…

A: To find the area of region R that lies inside the cardioid r=2(1+cos θ) and outside the circle r=3.

Q: 4. Sketch the curve of r2 = cos 20 and find the area that encloses it. Show your complete solution.

A: In polar coordinates,  r=x2+y2, θ=tan-1yx Converting the polar equation to cartesian coordinate…

Q: 4) Find the area of the region R that lies inside the cardioid r=(1+cos 0 ) and outside the…

A: We have to find area of the region R that lies inside the cardioid , r=(1+cosθ) and outside the…

Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

A:

Q: 3. Find the area of the region that lies inside the circle r - 1 and outside the cardioid r = 1 –…

A:

Q: Find the area of the region enclosed between y = 3 sin(x) and y =2 cos(x) from x = 0 to x = 0.5 %3D…

A:

Q: Find the area inside the curver = 2 cos 0 and to the right of r = sec 0.

A:

Q: 2. Find the area of the region that lies inside both curves = 4 sin(0) and r = 4 cos(0) O +1 2T - 1…

A:

Q: (3) Find the total area of the region trapped between y = sin x and y = cos x and lines x = and x =…

A: The equation of the curves are C1: y = sin(x) C2: y = cos(x) C3: x = π4 C3: x = 214 To evaluate: The…

Q: 9. Find the area of the region between y = sin 0 and y = sin e , between 0 = 0 ande = n/2. %3D

A: To find the area of the region between,  y = sin3 θ  and y = sin θ Between θ = 0 and θ = π/2 The…

Q: (b) Suppose we wish to estimate the area 3 Vĩ dx 2 using the Trapezium rule.

A:

Q: 1. Calculate the area of the region inside the curve r = 2(1- cos 0) outside the curve r = -6 cos 0.…

A: We have to draw the graph and calculate  the area of the region inside the curve r = 2(1- cos θ)…

Q: Find the area between the loops of the limacon r = Area = 5(1 + 2 cos 0).

A: We have to find the area between the loops.

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 specified region. Inside the circler= 3 sin 0 and outside the cardioid r= 1 +…

A:

Q: B. Find the area of the region bounded by the following: 18. common to r=3 cos 0 and *=1+cos 0

A: Given that r=3cosθ, r=1+cosθ

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

A:

Q: Find the exact area between a large loop and the enclosed small loop of the curve r = 1 + 2 cos(30).…

A: (1).    The given curve is: r=1+2cos3θ

Q: Calculate the area between the curves r2 16 sin 20 and p2 16 cos 20 .Show by drawing. %3D %3D

A: We will draw region first, then find the area using double integral

Q: 25) Find the areas of the regions eoclosed by the lines and curves y 2 sin x and v sin 2x, 0SIST

A: To find the area enclosed by the given curves: y=2 sin x and y=sin 2x, 0≤x≤π The area enclosed by…

Q: 3. The area between the two loops of the limacon r = 1+2 sin e.

A:

Q: 4 / Find the area of the region enclosed between the curves y%3= cos 2x, y=0, x-TT/4, x- TT/2 ? ans/…

A: we allowed providing one solution at a time. Please upload the rest questions seprately.   Question…

Q: Find the area of the region enclosed between y = 2 sin(x) and y = 4 cos(x) from x 0 to x = 0.67.…

A: We need to find area.

Q: Find the area common to the circle r = 3 and the cardioid r = = 3(1 - cos 0)

A: Figure of area enclosed by both curve÷

Q: 5) Find the area enclosed by the circle r = 3 cos 0 and the cardioid r =1 + cos 0.

A:

Q: 6. Determine the area of the region (a) outside the cardioid r =1+ sin ở and inside the circle r = 3…

A: Solution is provided here in the picture

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.