The lower, upper limit in the evaluation of the area of the region bounded by the two curves 2 y = x² and y = 9x – 14 respectively are -

Q: 2. Find the area of the plane region bounded by the curves y = x2 – 2 and y = x

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Q: Find the area of the region under the given curve from 1 to 2. 5 y = X° + 4x

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Q: Find the area of the region bounded by the curve y = xe and the raxis from x- 0 to x =3 0.5 -0.5

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Q: 2/ Find the area of the region enclosed by the curves y=lx) and 0on the interven-4] A3 B. D, IS

A: Given: Area enclosed by y=|x| and y=0 on the interval [-1,4]

Q: The lower, upper limit in the evaluation of the area of the region bounded by the two curves y = x…

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Q: The area of the region bounded by the curves y = I' and y = 2x is %3D 1/3

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Q: The lower, upper limit in the evaluation of the area of the region bounded by the two curves y = 2…

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Q: Find the area of the region bounded by the given curves. (22) y = cos x + 1, y = x, x = 0, x = 1

A: First of all we need to draw graph of all functions and then find out the common region and finally…

Q: Find the area of the region between the curves y = x2 +9 and y = 10 + 2x over the interval [-1,3].

A: Here we have to find the area of the region between the curves y=x2+9 and y=10+2x over the interval…

Q: Find the area with respect to y of the region bounded by x = y² + 2 , x = 0 , y =– 1, and y = 2. |

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Q: Find the area of the region bounded by the given curves. y = 1- 2 x2, y =|x|

A: Given: y=1-2x2y=x To Find: Area of the region bounded by the given curves.

Q: Find the area of the region bounded by the curves y=xy=x  and y=x2y=x2

A: First I have draw the diagram for given curves, then find the area between them. Area between curves…

Q: Find the area of the region bounded by the given curves. y = √x,  y= -3√x.  y= x- 2

A: It is given,Function 1: y= -3x1  OR x1 = y29                        (1)Function 2: y= x2- 2   OR x2…

Q: D Find the area of region bounded by the Curve y= Xe and X-axis From X=otox=4 %3D

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Q: The value of $ $(2xy - x²) dx + (x+y2) dy, where C is the enclosed curve of the region bounded by…

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Q: Find the area of the region bounded by the curves y = x² and y = - x² + 4x. 9/4 11/3 12/15 8/3 none…

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Q: a. Find the area of the region bounded by the curve y = x³ and the line y = 4x. ovis for

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Q: The area of the region bounded by the curve y = a° – 3x? – x + 3 and y = 0 is

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Q: Find the area of the region bounded by the curves y = y = -x² + 4x. 9/4 11/3 12/15 8/3 none of the…

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Q: Find the area of the region bounded by one loop of the curve x2 y*(1 – y²) %3D

A: The curve is given as , x2=y41-y2 The graph of the curve is

Q: Find the area of the region bounded by the curves: y = cos(nx) and y = -1 + 4x2

A: The region between these two curves is shaded below

Q: d the area of the region bounded by the curves y = 3x and y = x².

A: Given query is to find area bounded by the curves.

Q: /2y +6 5. Find the area of region bounded by the curves and *- y-1

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Q: 14. Find the area of the region bounded by these two curves: X = y' – 2y and x-y-4=0

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Q: Find the area of the region enclosed by the curve y=x²-3x³ + 2x² at interval from x=0 to x = 2.…

A: The graph of the curve y=x4-3x3+2x2 is To evaluate: The area of the region enclosed by the given…

Q: 3/Find the area of the region ecloseed by the curves y=cost and y=0 on the intervalL A-2

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Q: Find the area of the region that is completely bounded by the two curves f(x) = – x² – 3x + 19 an…

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Q: Find the area of the region bounded by the given curves. y = x², y = 4x – x² - ly=x²

A: We have to find area of bounded region.

Q: While evaluating the area of the region bounded by two curves Vy = z and y- 11z + 24 = 0, the values…

A: Given curves are: y=x   ............................(1)& y-11x+24=0  ..............(2)

Q: Find the area bounded by the curve x=16-v² and the curve x=y-5y+4 as shown in figure below. x = y² –…

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Q: Find the area of the region bounded by the curves: y = cos(nx) and y = -1+ 4x²

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Q: Find the area between the curves y = x² + 5x and y = 3– x² between a = -2 %3D and z = 0.

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Q: Find the area of the region enclosed between the curves y = x and x = y -6, and the region extend…

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Q: x = y² - 2y and x = 4y - y²

A: The given curves are; x=y2-2y and x=4y-y2 Now find the point of intersection between the given…

Q: 6. Find the area of the region bounded by the two curves of equat rens a) x=3-y² and f(x)= 3x (スー2)-…

A: Note:- In Part (a), you mention f(x) for 2nd curve but it is not mentioned for first curve. If i…

Q: The area of the region bounded by the curves 8x =y° and 8x = 2y+y2 -2y is

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Q: 2. Find the area bounded between the curves: y = x², y = 4 – 3x, and x = 2 %3D

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Q: The exact area of the region bounded by the graphs of y = x² + 2, and the x – axis from r = -1 to x…

A: Given that:

Q: Find the area of the region bounded by the curves y = x²y = x² and ² 01/2 02 O 1/3 O 2/3 = xy = x.

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Q: Find the area of the region between the curves y = x2 + 9 and y = 10 + 2x over the interval [-1,3].

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Q: = Compute the area of the region bounded by y hyperbolic or inverse hyperbolic functions. 1 √x²+16…

A: We compute the area of the region bounded by y=1/√(x2+16) over the interval [ 0,3 ] hyperbolic or…

Q: Sketch the graph of the given curves and find the area of the region bounded on the left by the…

A: Graph of x=3-2y2, that is gy=3-2y2 is a parabola as function g(y) is in the form of quadratic…

Q: 8. Find the area of the surface of the region generated by rotating the curve y = x³ from x=0 to x=1…

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Q: The lower, upper limit in the evaluation of the area of the region bounded by the two curves y = and…

A: Given curves are: y=x2 ............(1)y=10x-16   .........(2)

Q: Find the area of the region under the given curve from 1 to 2. 13 y = x + 4x

A: As we can calculate the area under the given by integrating the given function for the given…

Q: 3. Find the area of the region bounded by the curves y = x² and y = x/x+2. .

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Q: find the aRea of the Resion (5) bounded by the given cURves. J. Y=-13X+1 , X=0, X=4,4 X-axis |

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Q: Find the area of the region enclosed by the curve y=x2-2 and by the line y BO 2. y=x²-2 y=2 Co

A: The equation of the curve is:                                            y=x2-2  The equation of the…

Q: While evaluating the area of the region bounded by two curves V/y = x and y – 10x + 21 = 0, the -…

A: We will find interesting points.

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.