Find the total area of the shaded regions. 14 Q 4-2,12) 12- (2,12) 2. fy%3D3x ty= 10 -4- -2- y%3Dx to -군 6,

Q: Find the area of the shaded region.

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Q: Find the area of the shaded region. Ay 64- y 64-x2 48- Q 32- 16- -8 -6 -4 -2 2 4 6 8 10 -16- -32-…

A: The area under a curve, f(x) between two points, x=a and x=b can be found by doing the definite…

Q: Find the area of the region. y = 16 – x4 15 10 -3 -2 -1 1 2 3

A: Given:- y = 16-x4  To find:- Area of region bounded by curve and x axis

Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

A: topic - area under the curve

Q: Determine the area of the shaded region. 2.1 +2x 3.1 4.1 y-2x- y-2-

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Q: Find the area of the shaded region. y y= 9x- x² 20 15 (7, 14) 10 5 y = 2 x 4 6. 8 10 2.

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Q: Find the area of the region. y = 2x + 5,    y = 15 − x2,    x = −1,    x = 2

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Q: Find the area bounded by the arc square root x + square root y = 7, the x axis, and the line joining…

A: Given curves are                                                   1x+y=7, y=0, points (16, 9) &…

Q: Find the area of the shaded region. y 3 y = Vx 11, 1) x = 27 1 y = 10 15 20 25 2.

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Q: Find the area of the shaded region. y 3y= 2 x+ 16 (1, 6) 6 4 (2, 4) (-2, 4) y = 8 – 2x -4 -2 2 4 2.

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Q: he area bounded by y^2=4x and the line 4x-3y-4=0.

A: In this question, the concept of Integration is applied to determine the area bounded by two curves.…

Q: Find the area of the shaded region. y y3x² 3y 2 x+16 8 (1, 6) 4 (2, 4) (-2, 4) 2 y = 8 – 2 x -4 -2 4…

A: First we will divide the region in two parts.

Q: Find the exact area of the shaded region: (0, 4) y = 4 - x2 3 (3,-5)

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Q: Find the area of the unbounded shaded region. y = 8xe- y 2.0 1.5 1.0

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Q: Find the area of the shaded region. y =x4. 32 -2 -5- -10+ -15+ -20- 30+ 35- 40- y = -x 4 O 256 516…

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Q: Find the area of the shaded region. (-5е — 5) 2 y 14 (1, 5e) 12 10 y = 5 e 8 6. 2 y = 5xe -1.0 -0.5…

A: The area of the given shaded region which is bounded by the curve y=5ex , y=5xex2  and x=0  is…

Q: 2. Find the area of: (a) the region bounded by y = x^2, the x-axis and the line x = 2 (b) the region…

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Q: Find the area of the unbounded shaded region. y = 4xe-2x? y 1 0.5 2

A: Topic-Application of integration

Q: The shaded region has what area? 1.5 y = x 1 0.5 -0.5 0.5 1 1.5 2 2.5 3.5 4 4.5 1 -0.5 (x – 3) 2 y =…

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Q: Compute the area of the shaded region. y=-x(x-2) 3 3/4 13

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Q: over the triangular region Cut from the * quadrant by the line x+y =1.

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Q: 3 Reverse the or der of intagration and do not evaluate. xp hp 0, 3.3 Show the region.

A: To reverse the order of integration and do not evaluate.∫01∫x11y3+8 dy dx

Q: Find the area of the shaded region. y y=5x-x (3, 6) 4 2 y=2 x 1 2 3 4

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Q: Find the average value of(x,y)=2x^2y^2 over the rectangle R with vertices (−6,0),(−6,2),(6,0),(6,2)…

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Q: Calculate the area of the region bounded by the graphs of the given equations. 4) y =x°, y = 9x 5) y…

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Q: What is the area of the region in the first quadrant bounded above by y = -2x + 8 and below by y =…

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Q: Determine the area of the region bounded by y = 2x2 + 10 and y = 4x + 16. 28 24 y= 4x+16 20 16 12 y=…

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Q: Find the area of the shaded region. 2 (0,4) y = 4 - x (3,-5) 23 3 5/3 3.

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Q: Find the total areas of the shaded regions

A: according to given figure areaA of shaded region is given by A=∫01x13-x12dx…

Q: Find the area of the shaded region. y y = 9x-x 20- 15- (7, 14) 1아 5- y= 2x 10

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Q: Find the area of the region bounded by y = -4x + 9, y = 2x? – 11x + 9, and the lines x = -2 and x =…

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Q: Find the area of the shaded region. y 4 3 2 1 (1, 1) 2 y = √x y = 4 X 6 X = 8 8 X

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Q: How many square units is the area of the region bounded by the two curves y = x^2 - 4x and y = x^3 -…

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Q: Find the area of the shaded region. y 4 y = Vx 1 (1, 1) X = 8 1 2 4 6. 8 3. 2.

A: Subtract the lower function from the upper function and integrate the function between the limits 1…

Q: Find the total area of the regions enclosed by the two curves y = 4-x2 and y = -x+2 %3D and the two…

A: The given curves are: y=4-x2, y=-x+2 and the lines x=-2, x=3

Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: The region is bounded by the line y=6x, the x-axis, and the lines x=3 and x=6

Q: Find the area of the shaded region. y 4 2 y=V x ((1, 1) X= 8 y = X 4 6 8 1,

A: The region is bounded by the graphs,y=x3 and y=1x from x=1 to x=8

Q: Find the area of the shaded region. (9,3) x = y2 (0,0) (9,-3)

A: Using horizonal strip Established double integral

Q: yA y = 4 y X = 4 x = Vy

A: Given:- x=y/4  , x=√y , y=4  To find :- Area enclosed by given curves

Q: 2. Find the area of: (a) the region bounded by y = x^2, the x-axis and the line x = 2 (b) the region…

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Q: 5. Find the area of the region enclosed by y = 4 – x², y = 3x and r-axis.

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Q: While evaluating the area of the region bounded by two curves y√=xy=x and y−15x+54=0y−15x+54=0, the…

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Q: Find the area of the region bounded by the graphs of the equations. 3 y = 7 + Vx, X = 0, х %3D 8, у…

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Q: Find the area of the region in the first quadrant bounded by the line y=5​x, the line x=5​, the…

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Q: Find the area of the shaded region. y 3 y = Vx (1, 1) x = 8 2 8. 2)

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

Q: Find the area of the shaded region. y 3y= 2 x+ 16 (1, 6) 6 4 (2, 4) (-2, 4) 2 y = 8- 2x -4 -2 2 4)

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Q: Find the area of shaded region by using Trapezoidal rule YA 2.5 x = y 1.5- 1- y = In 2 0.5- x= e?y…

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Q: Find the area of the shaded region. 12) y = Jx - 3 (16,1) 16 (0, -3)

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Q: Approximate the area of the shaded region using the Trapezoidal Rule and Simpson’s Rule with n = 4.

A: Definition used -             Trapezoidal Rule-                   ∫abf(x)dx≈∆x2(f(a)+…

Q: Find the area of the shaded region    y = 5x - x 2  ,  y = x            ,  (x ,y )  =  ( 4, 4 )

A: The given equation of curves are: y=5x-x2. y=x Draw the area represented by the curves. The area…

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.