Q5 / Find the area of the triangular region in the first quadrant bounded by the x-axis and the curve x = y? x= y2 y = 2 X= 4

Q: Q4. : Find the area of the region R enclosed by the curve y=x+2. Y3DX2 and the line

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

A: SOLUTION-

Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y – axis and the parabola y² –…

A:

Q: Find the total area of the region between the curve and the x-axis. y= 2x-x2; 0sxs2

A: Explanation: Given curve is: y=2x-x2 Here x is from 0 to 2 To find the total area between the curve…

Q: Find the area enclosed by the x axis and the curve y= 4-x2

A: Find the area enclosed by the x axis and the curve y= 4-x2

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

A: Now the diagrammatic representation of the area is,

Q: Determine the area of region by y = x^2 + 4x and the y - axis

A: Area between the y=x^2+4x and y-axis is unbounded .  So, we will find the area bounded by the region…

Q: Find the area of the region under the curve y 3x +2x, the x-axis, x=0 and x 4. 0

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Q: Find the area bounded by the curves -x + y² = 8, x = -2y and y = -2.

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Q: Find the area between the curves y and y 3x + 2.

A: From y=x3, y=3x+2 solving for the points of intersections.…

Q: Q4/ Find the area of the region enclosed by the curves 4x² + y = 4 and x* - y = 1.

A: Consider  the curves  4x2+y=4x4−y=1

Q: Find the area in the first quadrant bounded by the curve y = 3x – x, the lines x = y = 2. 0 and

A: To find the area of the region bounded by the curve we use the formula Area=∫abf(x)-g(x)…

Q: Find the area enclosed between the curve y = 9 - x squared and line y = x + 7

A: This question is based on application of integration.

Q: Find the area of the region cut from the first quadrant by the curve x1/2 + y1/2 = a1/2.

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Q: Find the area of the region enclosed by the line y=4x and the curve y=x³ + 3x².

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Q: Q3/ Find the area of zone bounded by curves: y= x , y= 3x+8

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Q: Q3 Answer with all details, find the area of region in the first quadrant bounded on the left by the…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the area enclosed by the curve y = x 2 − 3 and the line y = 2x

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Q: . Find the area of the region bounded by the curves y = 2x? - 8x + 12 and y = -2x+ 12.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the area of the region enclosed by the line y = 4x and the curve y = x3 + 3x?

A: Given: y=4xy=x3+3x2

Q: Q4) Find the area of the region bounded by the lines ( y=x ), (y=2-x) &(x=1).

A: To find the area of the region

Q: Find the area of the region between the x-axis and the curve y = 8/(x² −4) for x ≥ 4.

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis. Answer:

A:

Q: Find the area of the region in the first quadrant bounded above by the curve y = 2√x and below by…

A:

Q: . Find the area of the region bounded by the two curves y = x3 + 3x2 + 2x and y = 2x? +4x.

A: As per Bartleby guidelines rule I am answering only first question because the second question is…

Q: Find the area of the region bounded by y = 2x? - 3x +2 the x axis and the vertical lines x= 0 and x…

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Q: Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

A:

Q: Find the area of the region enclosed by the curves y = 7 – 2x² and y = x² + 4

A: We need to find the area of the region enclosed by the curves y=7-2x2    and    y=x2+4. Let us plot…

Q: Q3/ Find the area of zone bounded by curves: y= x? y= 3x+8

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Q: Find the area enclosed by the given curves. y = 2x-x2,y 2x-4 31

A: Explanation of the answer is as follows

Q: Find the area of the region enclosed by the line y=4x and the curve y= x3 + 3x2

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Q: Find area of the region under the curve y = 3x³ – 5 and above the xt-axis, for 2 < x < 5. area =

A: Graph of the equation:

Q: Q4/ Find the area of the region enclosed by the curves 4x² + y = 4 and x* – y = 1 . |

A:

Q: Find the total area of the region between the curve and the x-axis. 7) y = 2x - x2; 0 sx<2

A: Given, The curve  y = 2x-x2   ;  0≤x≤2 We have to find the area of region between the curve and the…

Q: Find the area of the region bounded by the curves, y = -6, y = 6,the y – axis and the parabola y² –…

A:

Q: Find the area of the region bounded by the curve y?=4x and the lines x = 1 and x = 4.

A:

Q: Q3 Answer with all details, find the area of region in the first quadrant bounded on the left by the…

A:

Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y – axis and the parabola y? –…

A:

Q: Find the area of region enclosed by the curve y = x' -4 x +3 and the line y =3.

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Q: Find the area of the shaded region (using the area between two curves). y=x2 - 4 y=2x² •x - 6

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Q: Find the area of the region bounded by the curve y = e2x - 3e* + 2 and the x-axis.

A: The region is bounded by the graph y=e2x-3ex+2 and the x-axis.

Q: Find the area of the region bounded by the three curves y = x², y = 8 - x², and 4x - y + 12 = 0.

A: Given: y=x2y=8−x24x−y+12=0

Q: Q3/ Find the area of the region in the first quadrant that is bounded above by y = with respect to…

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Q: Find the area enclosed by the curve  x = t2 − 2t, y = square Root(t) and the y-axis.

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Q: 8 y = 2x and æ = Determine the area of the region bounded by y 4.

A: We need to determine the area of the region enclosed between y=8x , y=2x , x=4 Now, in the graph…

Q: Find the area between the curves: y = x3 – 12x? + 20x and y = -a3 + 12x2 – 20x

A: Solution )

Q: Find the area bounded by the curve y = 4x - x² and y = 3. Answer:

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Q: Find the area in the first quadrant bounded by the curve y = 2x^2 the y - axis, and y = 3

A: we have to find area in the first quadrant bounded by the curves…

Q: Find the area of the region enclosed by the two curves y = 2|x| and y = x² – 3.

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Q: Q1: Find the area of the region bounded by y= Vx, y v4-x and x-axis.

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.