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

Q: Find the area of the shaded region. y = V 1X1, 1) x = 27 10 15 20 25

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Q: Find the area of the shaded region. y = x - 32 y = -x4 Select one: A. 512 В. 2816 C. 256 D.

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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 1 y = x2

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

A: Given curve is y=x2+2 and y=x

Q: y y= 4x y3= 2 y345– x

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

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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: 23. (x – 1) dA; R is the region in the first quadrant enclosed R

A: Given: ∬R(x−1)dA=?

Q: Find the area of the shaded region. ¡y = x² + 1 ... 5 y = x 2 A B D

A: Area of a bounded region by curves is given by ∬dydx.

Q: Find the area of the shaded region. NOTE: Enter the exact answer. A = x = y 16 512 y? 16

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Q: What is the area of the shaded region? y = y = -2x*

A: We will take difference of both curves to find the area using integration.

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

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Q: Find the area of the shaded region. The image is not to scale. x = -c y x=d- y? Consider c=6, d=7.…

A: If f(y) and g(y) are two continuous function  on the interval [a,b]  and f(y) ≥g(y) on a≤y≤b , then…

Q: Find the area of the shaded region. y=2x2+x-6 y=x2-4 W

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Q: Find the area of the shaded region. NOTE: Enter the exact answer. x = y A = 6. 27 x = y? 6

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Q: 9. y. x = 2y x = y? – 3

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Q: Find the area of the shaded region.

A: Consider the provided region, Find the area of the region.

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: MacBook Air 3. O16 3. 2. 3. (E- (T'9T> 3. Find the area of the shaded region.

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Q: Find the area of the region enclosed by the curves x+y 0 and x+6y 80. The area of the region…

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Q: Find the area of the shaded region. y = x2 + 3 (2,7) (0,3) 23 A) 3 26 В) 3 22 25 D) 3

A: As per the guidelines we can solve 1 problem only.

Q: Consider the diagram below. B 3V2 Which of the following represents the best way to calculate the…

A: we can consider the shaded region as made of 2 segments. So we can apply the process of option 4 to…

Q: y = 1/x2, y=9, x=6 Find the area of the region?

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Q: ind the area of the shaded region. y= 2x? + x - 6 y=x2.4 3+ 2 19

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Q: Find the area of the shaded region. NOTE: Enter the exact answer. A = x = y 4 8 y? 4

A: We have to find the area

Q: Find the area of the shaded region. The image is not to scale. x=-cy x =d- y? Consider c=2, d=2.…

A: Solution:-

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

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Q: Find the area of the shaded region. Show your complete solution. r = 0

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Q: Find the area of the shaded region. NOTE: Enter the exact answer. y = x² + 1 A y = x 4

A: Please refer the attached image for complete solution. THANK YOU.

Q: y = x(x2 – 4)

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

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: Find the area of the shaded region. x = -y 2 x = 2 - -2 A B 10 3 2.

A: Given query is to find the area of the shaded region.

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

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Q: Find the area of the shaded region. NOTE: Enter the exact answer. y = x2 + 2 %3D y = x 4.

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Q: Find the area of the shaded region. y = x – 2 2+ y=V 1 2 3 4 | square units

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Q: Find the area of the shaded region. y = x² + 1 ... 5 y = x -1 2.

A: In given problem we find the area by using the Definite Integration .

Q: Find the area of the shaded region. NOTE: Enter the exact answer. y = x² + 4 A = y = x

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Q: Find the area of the shaded region in the figure below: x = (y- 1) *= 3-y T= 2Vy 2.

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Q: Find the area of the shaded region. NOTE: Enter the exact answer. x = y 1 y? 2 ||

A: From the given bounded region; First, we have to find the point of intersection between the curves…

Q: Find the area of the shaded region. y=x? - 2x 76 15 7 15

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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: Find the area of the region enclosed by the curves x+ y =0 and x+6y = 20. The area of the region…

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Q: Find the area of the shaded region. The image is not to scale. x=-Cy x=d- y? Consider c=1, d32.…

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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

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Q: Find the area of the shaded region. x = -y x = 2 – y? -2 A B 10 2. 2. 3.

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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.