Find the area of the shaded region. x = y 20 x = 1000 / y? 20

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. NOTE: Enter the exact answer. y = a? +2 A = y = x 3

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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. V2 y = csc e cot è 0- 3x - 2

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

A: Topic:- area under the curve and integration

Q: Find the area A of the shaded region where b = 9. y = |x| + -b A =

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Q: Find the area of the region enclosed by the graphs of: y? = 15 – x and x = 6. %3D

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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. NOTE: Enter the exact answer. y = x2 +2 A 2 y = x

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

Q: Find the area between the graph of y = 6x and the x-axis on the interval [-2, 2]. Write the exact…

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

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

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Q: r = V0

A: Given r=θ. The area of the polar coordinates is, A=∫12r2dθ Then, the area of the shaded region is,…

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 below. yA x= y? – 4y (-3, 3) x = 2y – y? Area =

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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: X = y 12 x = 216 / y? 12

A: Given curves are x=y   ...1x=216y2   ...2

Q: 9. y. x = 2y x = y? – 3

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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 below. у y =Vx 2 x=2 1 y=- x1 Area

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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 y= xV4 x y=0 2 y= 0 -2 SQuare units 21

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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: Find the area of the shaded region. y X = y 6 x = 27 / y? 6

A: *to find:- Area, A under the closed region. *concept:- take horizontal elemental strip of length dx…

Q: What is the area of the shaded region below? 16 -y = 2r² + 8 -y = x* NOT TO SCALE

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

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Q: x=(y– 13 2- x=3-y 1 T= 2Vy

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Q: Find the area of the shaded region. y x= 2 y = 2 e* y= 5 x– 1

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

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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: Find the area of the region enclosed by the curves. y = x? - 36| and y = * 36

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

A: We have to find the area of the shaded region of the figure given below.  Cleary the shaded region…

Q: Find the area A of the shaded region where b = 7. y = |x| + -b

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

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

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Q: Determine the area of the given region. x, The region in the first quadrant bounded by y = x and y =…

A: To Determine: the area of the given region in the first quadrant bounded by the two curves  Given:…

Q: Find the area of the shaded region. X = y 6 x = 27 / y2 6.

A: Area between the curve x=f(y) and x=g(y) on [a, b] is, A=∫abfy-gydy

Q: Find the area of the shaded region. r = v 0

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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 below. yA x= y? – 4y (-3, 3)– x= 2y – y? Area =

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

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: yA y = 8x y = 9 – x? y =

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Q: Find the area A of the shaded region where b = 4. y = |x| -b

A: Calculate the area of the shaded region where b=4.

Q: 4. Find the area of the region enclosed by the equations below. y = z? and y = 4 – 3x

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Q: What is the area of the shaded region in the graph below? x = 2y – y? 1 2.

A: Given curve is x=2y-y2  and interval [0,2]

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.