Find the area of the region bounded by the curves y = x +2x and y=-x² +4.

Q: find the area of the region that is enclosed between the curves y=x2+2x       y=x+2

A: The given curves are y = x2+2x and y = x+2.

Q: Find the area of ​​the region bounded by the y=x3 and y=2x-x2 curves.

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Q: Find the area of the region bounded by the three curves y = x^2 , y = 8−x^2 , and 4x−y + 12 = 0.

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Q: Find the area of the region bounded by the curves: a) y=2x and y = 8 from x =-2 to x=2

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: Find the area of the region bounded by the curves.  y = 8x2 and y = 1x

A: To find: The area of the region between the curve y=8x2 and y=x. Formula used: The area between the…

Q: Find the area of the region between the line y = 2x and the curve y = x²+ x – 2

A: y=2x --------(1) y=x2+x-2 -------(2) For points of intersection…

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

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Q: The area of the region bounded by the curves y=x and y= 20-x² is

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Q: The area of the region bounded by the curves y =x and y= 20-x² is

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Q: y2 = 4 – x and y² + y = x + 2

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Q: find the area of the region bounded by the curves y=x3 and y = x² between their intersections.

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Q: The area of the region bounded by the two curves y = x“ and y = 4 is

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Q: Find the area of the region bounded by the curve 2-4r and the lines x = 1 and x = 4.

A: To find the area

Q: Find the area of the region bounded by the curves y = x ^ 3 - 12x, y = x ^ 2.

A: y = x ^ 3 - 12x, y = x ^ 2.

Q: Find the area of the region bounded by the curve y=x^2−1 and the line y=15.

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Q: Determine the area of the region bounded by the curves y = x4 - x2 and y = x2 - 1

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Q: Find the area of the region bounded by the curve y = x2 and the line y = x + 2

A: We have to find the area

Q: Find the area of the region between the curves y=x^3, y=-x, and y=1

A: Area=14 sq.units

Q: Find the area of the region bounded by the curves y = 2x^3 − x^2 − 5x and y = −x^2 + 3x.

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Q: Find the area of the region bounded by the curves: y = 2x and y = x² – 4x

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Q: Find the area of region bounded by the curve y=x²-2x and y=-x²+4

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

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Q: Find the area of the region bounded by the curves x-y+ 4y = 12x, x = 1, x = 4, and the x-axis %3D

A: First we will draw the graph  and we will find the area by using following formula Area A = double…

Q: Find the area of the region enclosed by the line x = 2y and the curve x = y3 - y?

A: To calculate the area of the region bounded by the curves x=fy and x=gy, use the formula…

Q: Find the area of the region bounded by the curves. y = x² and y = -x² + 4x

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Q: 2 y = x - 3x, y=x 3r.

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Q: Find the area of the region between the curves y = x + 1, y = 9 – x², x = -1, and x :2. %3D Area…

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

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Q: Determine the area of the region bounded by the curves y = ₁, y = 2x and x = 4

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Find the area of the region bounded by the graphs of the equations y = x² and y = vx.

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

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

A: We will use double integration to solve this

Q: Find the area of the region between the line y = 2x and the curve y = x2 + x − 2

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Q: Determine the area of ​​the region bounded by the curves y = x3  , x + y = 2 and y = 0

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Q: Find the area of the region bounded by the curves y = 1 (x+1)21 2 y = 4 and

A: Please refer to the image below

Q: find the area of the region bounded by the curves y=12x/(x^2+4) the x-axis x=1 and x=4

A: The region corresponding to the equations is given below, Consider an elemental vertical strip of…

Q: Find the area of the region between the curves y=x(2−x) and y=2 from x=0 to x=2

A: To find the area between the curves

Q: Find the area of the region bounded by the curves y=−3x, y=√x  and y=6

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Q: Find the area of the region bounded by the graphs of y = x +6x, x = 0, x = 2, and the x-axis.

A: Answer

Q: Find the area of the region bounded by the curves y = x2 and x2 + y = 4x.

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Q: Find the area of the region bounded by x = 2y – y² and x = -y.

A: NOTE: Refresh your page if you can't see any equations. .

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

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Q: Find the area of the region bounded by the curves x + y = 0 and x = y² + 3y.

A: NOTE: Refresh your page if you can't see any equations. . given equations are so the first…

Q: find  the area of the  region bounded by the  curves y²=4px and x²=4py

A: To find the area.

Q: y = 2x 2 − 8x + 12 and y = −2x + 12.

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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: Find the area of the region bounded by the curves y = 6 – x² and y = x + 4.

A:

Q: Find the area of the region bounded by the curves y = 6 – x² and y = x+ 4.

A: intersection  6-x2=x+4x2+x-2=0x2+2x-x-2=0x(x+2)-1(x+2)=0(x+2)(x-1)=0x+2=0 or x-1=0x=-2 or x=1⇒-2≤x≤1

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

A: Given:          x2=y41-y2         x=±y41-y2         x=y21-y2 The graph is symmetric about the…

Q: Find the area A of the region bounded by the line y = x and y = 6 – x²

A: Area between curves

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.