Find the area of the shaded region shown in the graph. Ay y320 sinx 20 v%3D20cosx 13 IN

Q: O Find the area • y- 1x, y- e* %3D

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Q: Find the total areas of the shaded regions

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Q: 4. Determine the area of the shaded region. -y =Dx y= x²2

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Q: Q1. Calculate the area of the region lies inside the diagram (r= 4 cos 20) and outside the circle (r…

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Q: Find the area inside the circle r = -3a cos0 and outside the cardioid r = a(1- cos 0).

A: Area Inside the circle and outside the cardioid can be calculated by using integration concept and…

Q: Find the area of the shaded region in the following graph: y 2 y = sec? y = sin(4x) T/8 T/4

A: The figure is given by To evaluate : The area of the shaded region.

Q: Find the area of the shaded region. V2 y = csc e cot è 0- 3x - 2

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Q: EX Find the area of the s had ed of fig show belwo usetng dxdy X=-1 DZ D3

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Q: Find the area of the shaded region shown below. YA y = -x? + 4x y = x2 - 2x

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Q: Find the area of the shaded region. r = 6+5 cos

A: Introduction: The formula of the area inside the curve r=f(θ) is given by, A=∬rdrdθ Where limit of…

Q: Find the area of the shaded region 1 y = x2

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Q: Solve this attachment.

A: From the figure, the integral to obtain the area can be represented as, ∫-11y2-2-eydy

Q: d) Evaluate the area of the shaded region. y y =x'+1 -1 1

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Q: Find the area of the given region. y = cos x

A: To calculate Area : y = cos x Area = ∫x=0x = π/2y dx

Q: Find the area of the shaded region, if it exists. (If an answer does not exist, enter DNE.) y -6 x…

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Q: mine the area of the given region. y = x + sin x 4 X 4 A 3 2- +

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Q: What is the area of the shaded region? y = 2 2 x = TT y = 1 + cos x

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Q: Find the area of the given region.

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Q: Find the area of the region enclosed y = 7e¯ 7 and x = 0.

A: In this question we will simply use the basics of calculus i.e application of integration. We will…

Q: Determine the area of the given region. y = x + sin x 4 3. 2 1 -ele

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Q: B: Find the area of the shaded region show y y =1+x X=-1- y=-1 Fig(1)

A: According to the given below figure:  area of the shaded region is…

Q: Sketch the region enclosed by y=e^4x,  y=e^8x and x=1. Find the area of the region.

A: Given curves are  y=e4x, y=e8x and x=1. The graph is

Q: Q5 Find the area of region enclosed by the r=1-e cos 0

A: We know that  the area of a sector of a circle is 12α r 2 , where α is the angle subtended by the…

Q: Find the area of the shaded region, if it exists. (If an answer does not exist, enter DNE.) y 1 -7x…

A: The definite integral of the function gives us the area under the curve of that function between…

Q: Find the area of the shaded region. y = X - 3 (16,1) 16 (e,-3)

A: We first find where the curve cuts the x-axis

Q: Find the area of the shaded region shown in the graph. Ay Q y = 22 sin x 22 v = 22 cos X

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Q: Find the area of the shaded region. =3 sece tan e

A: To find the area of the shaded region

Q: Sketch the figures and show step by step solutions. Find the area between the curve y = x3 – 6x2 +…

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Q: Find the area of the given region. y = x + cos x

A: To Determine: Find the area of the given region. y = x + cos x Given: we have a function   y=x+cosx…

Q: Find the area of the shaded region shown in the graph. y= 15 sin x 15 y= 15 cos x

A: Integration gives the function whose derivative is given. Integration is nothing but adding slices…

Q: Find the area of the following shaded region. y = 1 y = cosx

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Q: 25. yA y = y = V1 – x

A: We have to find the area of the shaded region of the image.

Q: B) Find the area of the region enclosed by the Parabola y = 2 – x2 and the line y + x = 0 ?

A: The region is bounded by y=2-x2 and y+x=0

Q: Find the area of the shaded region. r= 4 + 3 sin e

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Q: 28. y A y = sin x 1 TT y = sin 2x

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Q: Find the area of the shaded region

A: Required area is,

Q: Find the area of the shaded region shown in the graph. Ay y = 11 sin x y= 11 cos x 2

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Q: (b) Find the area of the shaded region y=1 y=5-x^2

A: We have to compute the area bounded by the curve y=5-x2, the line y=1 and the y-axis. We will use…

Q: What is the area of the region in the first quadrant enclosed by the graphs of y = sin (2x) and y =…

A: To find the area of the region in the first quadrant enclosed by the graphs of y=sin(2x) and y = x…

Q: Q1. Calculate the area of the region lies inside the diagram (r = 4 cos 20) and outside the circle…

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Q: Find the area of the shaded region in the diagram given below. y = sin(2r) 6 y = cos(x)

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Q: What is the area of the shaded region? y = sin x TT ST 6

A: From the given region; So, The point of intersection between the curve and line is:…

Q: a) Find the area of the shaded region. 1) ii) y= T 2x=2-

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Q: Find the area of the shaded region. r2 = sin(2Θ)

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Q: Find the area of the shaded region shown in the graph. Ay y = 27 sin x 27 y= 27 cos x

A: Solution :-

Q: 1. AY -x² +1 y=x

A: we have to find out

Q: y 2 y = sec? x y = sin(4x) → X T/8

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Q: r=2a+acos 20 A r=sin 20

A: The polar curves do not intersect at any point. The area between the curves is the shaded region.

Q: Find the area of the shaded region in the following figure y = sin x 5п

A: Find the functions f (x) and g (x).

Q: Find the area of the shaded region. Ay 42 = 4 csc e cot e 0- 3x 4 -4/2 of

A: Consider the given graph. The shaded region is bounded above by the straight line parallel to the…

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.