Find the area of the shaded region. (We suggest that you use technology to check your answers.) y y = x - 2 x + 1 + x y =5 – x² 2.

Q: Find the area of the shaded region. y = JX - 3 (16,1) 16 (0,-3) Select one: A. 22 В. 38 3 O C. 16 D.…

A: Area of shaded region can be find as follows

Q: Q5/ Find the area of the region in the first quadrant that is bounded above by y = √x and below by…

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Q: Find the area of the shaded region. y =x+ - 2x3 1+ y = 0 -1 square units 2. 2.

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Q: Find the area of the shaded region. (-11/4, 11/2) 10 y 8 x = y² - 6 y 6 4 -2 x = 5 y-y² 5

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Q: Q3:B/ Find the areas of the regions enclosed by the line and the curve y = x* – 4x? + 4 and y = x?

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Q: Find the area of the shaded region. y2 +x=2 y-x 0 f the following can be used to area of the shaded…

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Q: y y= 4x y3= 2 y345– x

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Q: Find the total area between the region and the x- axis. y = x3 – 3x? + 2x -1 sxs2

A: Consider the curves, y=x3-3x2+2x  ;       -1≤x≤2

Q: y=V.r+ 2 www r= 2

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Q: A y y = x2 + 1 y = x -1 2

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Q: b) Find the area of the shaded region. 1) ii) y= T x=-y 2Fx= 2- y²

A: we have to find the area of the shaded region.

Q: The area formed by the boundaries y=1, x=2, and y=e-x is closest to: a.1.586 b.2.746 c.1.135 d.3.542

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Q: Find the area enclosed by the x-axis and the curve y=4-x2. A 18 square units 32 B square units 3 ©…

A: topic - area under the curve

Q: Find the area of the shaded region below. x= y? – 4y (-3, 3) x= 2y – y?

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Q: The area of the shaded region is x3 + Vy = 1, 0<Isl Select one: a. 3 O b. 3 3 4 d. 9 14

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Q: Find the area under the curve y= 3x° that is between the lines x = 1 and x= 3. The area under the…

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Q: Find the area of the shaded region.

A: Given the polar curve r=θ

Q: Find the area of the shaded region. y 2 x = y? – 9 y = 1 x = eY -10 -8 -6 -4 -2 2 4 y = -1 -2

A: Given

Q: ind the area of the shaded region. y 2 x = y - 6 y = 1 x= e -4 -2 2 4 H y = -1 -2 -31

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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. y x = y -8 -6 -4 -2 4 Hy=-1 2.

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Q: Find the area of the region in the first quadrant that is bounded above by y = vx and below by the…

A: Given curves are y=x   .......1y=x-2    .......2

Q: Q-3: Find the area of shaded region in the shape: y = x2- 6x + 5 3 5

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Q: Find the area of the shaded region below. у y =Vx 2 x=2 1 y=- x1 Area

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Q: Find the area of the shaded region. 15) y=-x4 y = x2 - 2x C) 2 76 D)- 15

A: From the given graph. Use the double integration method to calculate the bounded…

Q: Find the area of the shaded region below. yA x= y² – 4y (-3, 3) x = 2y – y² X :

A: The region is bounded by the graphs x=2y-y2 and x=y2-4y

Q: Find the area of the shaded region. The image is not to scale. x=-Cy Ay x=d- y? Consider c=3, d34.…

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Q: Find the area of the shaded region below. y = 3x - 3 y=-x + 3x +6 WCOLLEGE KL

A: We have to find the area under the curves.

Q: y=x² +2x+1 and y = 3x +3 The area of the plane region is?

A: "Since you have asked multiple questions, according to our guidelines we will solve only the first…

Q: y = 2x and y = 2x^2 − 4 , find its area.

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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: Find the area of the shaded region. y 31 x = y - 4 y = 1 x= e -2 2 4 y= -1

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Q: 4. x= y² – 4y (-3, 3) -4 Find the area of the shaded region. x= 2y – y?

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Q: Find the area of the shaded region. y = -x3 + x2 + 16x and y = 4x %3D 30 254 20 IS 104 y 4x 20 25 30…

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Q: b) Find the area of the shaded region. 1) ii) アー =-y 2Fx=2-

A: 1. Required area is, ∫04x dx+∫04-14x dx=∫04x12 dx+14∫04x dx=x323204+14x2204=23432-0+148-0=238+2=223

Q: Find the area of the shaded region. x = y² - 4 -2 y 3 -3 y = 1 x = e² 2 y = -1 4 X

A: Given graph:-

Q: a) Find the area of the curve x²/3 +y2/3 = a²/3 %3D

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Q: Find the area of the shaded region. 1) y = X - 3 (16,1) 16 (0,-3) 29 A) - 38 16 B) D)- 3

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Q: Find the area of the shaded region below. y x = y² – 2 y=1 x=e> y=-1 Area =

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Q: Determine the area enclosed by the curve r² = 4a²cos3θ a. 4a² b. 8a² c. 16a² d. a²

A: To find the area enclosed by the curve r2=4a2cos3θ

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 below. x = y? – 4y (-3, 3)

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Q: Find the area of the "triangular" region in the first quadrant that is bounded above by the curve y…

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Q: Find the area of the shaded region below. YA y A x = y² – 4y (-3, 3) – x = 2y – y? Area =

A: Here we have to find the area of the shaded region.

Q: problem in photo attached

A: Given that the curve is bounded by the curve x = y2 – 2 to x = ey and y = – 1 to y = 1.

Q: Find the area of the shaded region. NOTE: Enter the exact answer. y = x2 + 2 A = 2 3

A: Explanation of the answer is as follows

Q: The area of the shaded region: y-24 -1 (1.2) 2 3 5n

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Q: Find the area of the shaded region below. y A x= y² – 4y (-3, 3)- x = 2y – y?

A: Using the method of Integration

Q: Find the area of the shaded region below. y A y= 5x – x² (4, 4) y = x Area = %3D

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

Q: y1=x2+2x+1 y2 =2x+5 Find the area of shaded region

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.