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

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

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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 bounded by the curve y=1- and the x- axis.

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Q: Find the area of the region bounded by the curve y = x2 + 3x + 2, x = 0, x = 2, and x axis

A: Solution

Q: Find the area bounded by the curve x y2 +2y and the line z = 3. %3D

A: Given :                curve x = y2 + 2y and the line is x = 3 To find :               The area…

Q: Find the area bounded by the curve y = x 2 and y = 2 − x 2

A: To find area bounded by the curves y=x2 and y=2-x2.

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

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Q: Find the area of the region bounded by the curve y = x^3 + 3x and the lines x = −2, x = 2 and the…

A: Topic = Application of integration

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: Determine the area bounded by the curves x^3 - y = 0 and y + 3x^2 - 4 = 0 using a vertical element

A: The area is bounded by the given curves x3-y=0 and y+3x2-4=0. The main objective is to determine the…

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 a region bounded by the curves y= x^3, y= x ln(x^2), x=1 and x=2

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Q: Find the area of the region bounded by one loop of the curve y"(1 - у?)

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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 under the given curve from 1 to 6. x2 + 6 y = 7x — х2

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Q: Find the area bounded by the curve y=x^2 − 4, the lines y = 0 and x = 4

A: The graph is shown below:

Q: Find the area of the propeller-shaped region enclosed by the curve x - y3 = 0 and the line x - y =…

A: x-y3=0  &  x-y=0⇒y3=x  &  y=x⇒y=x13  &  y=x Now the diagrammatic representation of the…

Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² - 4 = 0, using a vertical element.

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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 regions bounded by the curves y = x 3 , y = x .

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Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: I have shaded the area green which is to be calculated

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 bounded by the given curves y=8x3+7 and y=8x+7

A: Given,           The curves are y=8x3+7 and y=8x+7.

Q: Find the area of the region bounded by the curves x = y3 - y2 and the line x = 2y. %3D

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Q: Find the area of the region between the line y = −x and the curve y = x2 + x − 3

A: Area of the region is 32/3

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

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Q: Sketch the region enclosed by the given curves and calculate its area. y=4-x to the power of 2, y=0

A: The given equation is

Q: Find the area of the region bounded by the given curves. y = 3x2 In(x), y = 12 In(x)

A: Find the area bounded by these curves.

Q: Sketch the region enclosed by the given curves and find its area. x = y4,  y = square root of (2 -…

A: We first sketch the region using a graphing calculator

Q: Find the area of the region bounded by given curves. 1. y +4x = 0 and x+2=0

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Q: Find the area of the the Curves bounded region x +y=O by X+y² =2

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Q: Find The Area Enclosed by the Curve x=7²-2t,y-VE and the Y-pris

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Q: Find the area of the region bounded by the curves x = y + 3 and y = x – 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: 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 region bounded by the given curves. y = 9x In(x), y = 36 In(x) %3D

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

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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 curve y=x^2-3x the x-axis and the lines x = 1 and x = 2.

A: This question is based on application of integration.

Q: Find the area of the region bounded by the curve y=1. and the x-axis.

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Q: Find the area of the region bounded by the curves y= x2 x3−3x and y= 1 x3−3x on the interval…

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Q: Find the area of the region bounded by the given curves. y = 6x2 In(x), y = 24 In(x)

A: Graph them using a graphing calculator. The graphs meet at x=1 and x=2 Blue curve is y=24ln(x) Red…

Q: Find the area of the region bounded by a curve y = x^2-3 and y =5-x^2

A: Consider the provided curve, y=x2-3  and y=5-x2 Find the area of the region bounded by a curve.…

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

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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.