5.Find the area Hhat is incide r=4 and autside rz 4-2sin &

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: 2)Find the area between y2=x and y=X-2 by using: a) Vertical strip. b)Horizontal strip.

A:

Q: ind the area under the given eurve y = Vメ + 4: from X=0 to メ= 16 ニ

A: Here we have to find the area under the curve y=x+4; from x = 0 to x = 16

Q: 15. Sketch the region enclosed by the lines x = 3 and y = 1 and the curve xy = 9, and find its area.

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given…

Q: 4. Find the area common to the circles x2 + y2 = 4 and x2 + y2 = 4x.

A:

Q: Find the area that is inside both r = 3 + 2cosθ and r = 3 −cosθ.

A: Area between r=f(θ) & r=g(θ) is defined as, A=12∫abf(θ)2-g(θ)2dθ

Q: 2- Find the shaded area of the regions in the figure below 21 y = sec2t y = 1-1 TT 4

A:

Q: . Find the area of the region bounded between the circles x? + y? = 4 and (x – 2)2 + y? = 4.

A: Area between curves

Q: Find the area of the region that lies inside the circle r = 1 and outsidethe cardioid r = 1 - cos θ.

A:

Q: Find the area inside one leaf of the three-leaved rose r = cos(30), as scen here: -0.4 -0.2 0.2 0.4…

A:

Q: between

A:

Q: Give area of the region enclosed by y and y = 0 from x = 1 to x = 3. 2 A. 2 В. 3.4 С. 1.5 D. 1

A:

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 of the regi on. X = 4¢3- t2 y= t* + 2t?

A:

Q: B) Evaluate S Ln z dz around the circle | z| = 2 %3D

A:

Q: Find the area bounded by the given curves and lines. 1 y? (2–æ)³ 3

A: We have to find area

Q: 4] [] Find the area of the region R in the first quadrant enclosed between the circle x2 + y? = 9…

A:

Q: Evaluate the integral o dz where C is the circle |2| = 2. 22 + 9

A:

Q: Find the area of the region inside the circle r = 4 cos θ and outside the circle r = 2.

A:

Q: 2- Find the area f the negion cut from the trst quadrant by the regson r= l+ Sino?

A: From the given problem:   r=1+sinθ   Given first quadrant it means:   θ→0 to π2r→0 to 1+sinθ   Now…

Q: Calculate the area outside the r=8sinθ curve and inside the r=4+4sinθ curve. Area=?

A: Calculate the area outside the r=8sinθ curve and inside the r=4+4sinθ curve.

Q: - Find the area of the negion that inside (i=3sin@) eind also In side (rz = + sin@) ?

A: To find the area of the region inside r1=3sinθ and inside r2=1+sinθ

Q: 11. Find the area of the region enclosed by x+y? = 0 and r+3y? = 2.

A:

Q: Give area of the region enclosed by y and y = 0 from x = 1 to x = 3 2 А. 2 В. 3.4 С. 1.5 D. 1

A:

Q: Find the area of the region inside the circle r=5sinθ and outside the limacon r=2+sinθ

A:

Q: Find the area bounded by the parabolic arc Vx + Jy = 7 and the chord joining (9, 16) and (16,9).

A: Topic = Application of integration  Area = 7/3

Q: 13. The area which is inside the circle r = 10cos O and to the right of the line r = sec O:

A: 13. The given curves are r=10 cosθ and r=secθ To find: area of the region bounded by the given…

Q: find the area between r=1 and r=1+2cos(2θ)

A: The given curves are,

Q: Find the area bounded by y= (11 - x)1/2, the lines 3x = 2 and x = 10, and the X-axis. 19.456 sq.…

A:

Q: Find the area between y = x + 11 and y = 3x + 2 between x O and x 2. %3D |3D Enter the exact answer

A: Given:       y=x+11       y=3x+2 over interval 0,2 The area between curves is the area between a…

Q: Find the area bounded by the curve (p^2)=16cosθ

A: We have to find the area.

Q: Now, the area is given by I((6 - 6y2) – (6y2 – 6)] dy = dy.

A:

Q: Bm 11 2元

A: we need to find the integral of the function in the given limits to get the

Q: 2. Find the area of the region enclosed by æ + y? = 0 and ¤+3y² = 2.

A:

Q: 10- Evaluate JS where E is the region that lies inside the cylinder x² + y²dV E x? + y? = 16 and…

A:

Q: of the region en and y =x? +4

A: 2. Given curve is: y=-x2-2x When y = 0 we get, -x2-2x=0⇒xx+2=0⇒x=0 ; x=-2 Then the area is:…

Q: Find the AREA and shad the CURVE 2 To the Right oF OF 2= 3.1t ( Outside oF and Z=-1. 32 2ニ-2.05 To…

A:

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

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Find the area enclosed by the given curves. y = 2x - x 2, y = 2x - 4 O 32 O 34

A: The given question can be solved as shown in step 2.

Q: d the area of region between twe nctions flx)= oinx, Sc)=cosax,-LXLI

A:

Q: Find the area that enclosed by the circle r-2sin 0 for 4 ≤ 0 ≤T/2 | (+-#) V=2sin o ty

A:

Q: Consider the following shaded region. yA y=ax-x y=bx Find the area S of this region if a = 4, b = 3.…

A:

Q: Of the expressions w could be correctly I to compute the area ded by graph Y=10x- and line y=2x ?

A: Please refer to the image below

Q: Find the area between the paral x = y? – 1 and x = 2y? – 2

A:

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

A: As you post multiple questions According to the guideline I only solve the first problem please post…

Q: 7. Evaluate sin(x² + y?)dxdy where R is the region inside the circle x² + y? = T.

A:

Q: ind the area between the two curves: y = x2 and y = 4x + 5 -symbolic formatting help

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.