Find the Area of the region bounded by the given curves : 1) r = 3+ 2sin0 2) r = 2 – 2cos@

Q: Sketch the region enclosed by the curves and find its area. 1 y = 9x² ,y = 9Vã,x = - and x = 1 %3D…

A: since you have posted multiple question in this question so i have solved first question as per our…

Q: Sketch the region enclosed by the curves and find its area. 1 y = 2 VI – 49x2 NOTE: Enter the exact…

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Q: Find the Area of the region bounded by the given curves : 1) r= 3+2sine 2) r = 2-2cose

A: r=3+2sinθr=2-2cosθ Then, 3+2sinθ=2-2cosθ1+2(sinθ+cosθ)=0θ=65.71,-24.29

Q: Sketch the region enclosed by the curves and find its area. 1 х — 0, у — 1, у — е NOTE: Enter the…

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Q: Sketch the region enclosed by the following curve and find its area. x = y^4, y =√2 − x, y = 0

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Q: 31. y = x', y= 2 – |x|

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Q: Sketch the region enclosed by the curves and find its area. y = 7x ,y = 7Vx, x = - and x = 1 Enter…

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Q: Sketch the region bounded by the curves y = vx + 4 , y=x +2 and evaluate the area.

A: Given Curves are     y = x+4   and    y = x+2  first equation can also be written as  x = y2 -4 now…

Q: Sketch the region enclosed by the curves and find its area. 1 Y = 2 V1 – 25x²' NOTE: Enter the exact…

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Q: Sketch the region enclosed by the curves and find its area. y = e", y= e3*, x = ln 2, x = lIn 3 In…

A: This question is based on application of integration.

Q: Sketch the region enclosed by the curves y = x? – 1 and y =1+x. Hence find its area.

A: We will find out the required value.

Q: Find the area of the region enclosed by the given curves.  y=2cos(3x), y=2sin(6x), x=0, x=π/6

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Q: 1. y = a2, y = Va, = x2, y = Vr. on the interval 0.25, 1]

A: The objective is to find the area enclosed between two curves.

Q: Sketch the region enclosed by the curves and find its area. y = cos 2x, y = 0, x: 4' 2 NOTE: Enter…

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Q: Sketch the region bounded by the given curves, then find its area. 2. x = y2, x = y +6

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Q: Sketch the region enclosed by the given curves andfind its area. y = x2 ,y = 4x - x2

A: Let us find the point of intersection by equating the two curves  x2=4x-x2 x2+x2-4x=0 2x2-4x=0…

Q: Sketch the region bounded by the given curves, then find its area. 1. y = x², y = 2x

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Q: Sketch the region enclosed by the curves y=2x, y=〖2x〗^2+x-3, then find its area.

A: The two curves are :                                    y=2xy=4x2+x-3 To determine:…

Q: Draw the region bounded by the curves r=√(3cosθ) and r=3sinθ and find its area.

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Q: Sketch the region and find its area (if the area isfinite). S = { ( x, y) |   -2< x <= 0  , 0…

A: The sketch will be as follows

Q: Sketch the region enclosed by the curves and find its area. y = 9r° ,y = 9/ñx = andx = 1 = 9Vã.x…

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Q: Sketch the region enclosed by the curves y = x² and y = 4x – x² and find its area.

A: Plot the 2 curves and find the area A to be calculated. The shaded region between the curves is the…

Q: Sketch the region enclosed by the curves and find its area. cos 5x, y = 0, x = x = 10' 5 NOTE: Enter…

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

Q: Sketch the region enclosed by the curves and find its area. y = e", y = e, x = 0, x = In 2 NOTE:…

A: The region is enclosed by the curves y=ex, y=e3x, x=0 and x=ln 2

Q: Sketch the region enclosed by the curves and find its area. y = cos8x, y = 0, x = π/16, x = π/8

A: Given: y = cos8x, y = 0, x = π/16, x = π/8

Q: Find the area enclosed by the given curves y = 8x2 – 2 and y = 9 cos(Tx). You may find it useful to…

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Q: Sketch the region enclosed by the curves and find its area. y = 3r° ,y = 3ñx =and x = 1 = 3x² ,y = 3…

A: Topic = Application of integration  Area = 49 / 64

Q: Sketch the region enclosed by the given curves andfind its area.   y - cos πx    , y=4x2- 1

A: The given curves are y=cosπx   and  y=4x2-1. Sketch the region enclosed by the above curves as shown…

Q: y =x.y = x, x> 0 1 1 y : X у —х, у — —х, х > 0 4

A: we need to use integration to find area between curves

Q: Sketch the region enclosed by the given curves and find its area. y = x²,y = 4x – x²

A: Given y=x2 ,y=4x-x2

Q: Sketch the region enclosed by the curves and find its area. 1 Vī 1 – x² y = 2 NOTE: Enter the exact…

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Q: 4. у%3D 2х—х2, y = 2x² – 4x

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Q: Sketch and find the area of the region that lies inside the curve r = 4 + 3cose .

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Q: Sketch the region enclosed by the given curves andfind its area.       y +x = 3     , y = 2  x 2  ,…

A: The given curves are x+y=3 , y=2x2 and y=14x2 , x≥0. To sketch the curve and find the area. The…

Q: Sketch the region enclosed by the curves and find its area. y = cos 11x, y = 0, x = x = 22 11 NOTE:…

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Q: Sketch the region enclosed by the curves and find its area. 1 y = 2 VI- x2 NOTE: Enter the exact…

A: Solution

Q: Find the Area of the region bounded by the given curves : 1) r = 3 + 2sine 2) r = 2- 2cose

A: we know in the polar form we imagine the area is made of triangles(with their apex at the origin)-…

Q: Sketch the region enclosed by the given curves andfind its area.    x = 2 y 2  , x =  4 + y 2

A: Definition used -    The area between curves -                        A=∫ab(f(x)-g(x))dx

Q: Sketch the region enclosed by the curves and find its area. 1 y = 2 V1 – 49x² NOTE: Enter the exact…

A: Given : y = 1/√(1 - 49x²) and y = 2

Q: 23. y = 2x, y =}r

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Q: 3 = 2y and a – 15 = (y – 6)², and compute its area. Sketch the region enclosed by the curves – A =

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Q: Sketch the region enclosed by the given curves andfind its area. y = 12- x 2   , y = x2 - 6

A: Given curves are y=12-x2y=x2-6

Q: Sketch the region enclosed by the curves and find its area. 1 y = y = 2 VI– 9x2* NOTE: Enter the…

A: Calculation of Area

Q: Sketch the region bounded by the given curves, then find its area. 1. у%3D х*, у%3D2х

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Sketch the region enclosed by the given curves andfind its area.       y =4 x 2  -1    , y =   cos…

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Q: Sketch the region enclosed by the given curves andfind its area.   y =cos x , y= 2- cos x  , 0 ≤ x ≤…

A: Given: The region enclosed by the curves  : y=cos(x)y=2-cos(x)           0≤x≤2π We have to sketch…

Q: Sketch the region bounded by the given curves, then find its area. y = x2 - 3x, y = x

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Q: Sketch the region enclosed by the curves and find its area. 1 y = 2 VT 1 – 25x2 NOTE: Enter the…

A: Solve by sketching graph

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.