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

Q: Find the area of the region bounded by the curves 1 y y = 4 and the x-axis using vertical strip.…

A: The given curves are y=1x+82 and y=4.

Q: Sketch the region bounded above by the curve 6xe−x6xe-x, the x-axis, and x = 3, and find the area of…

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

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

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Q: Find the area of the region bounded by the curves y= 2² - 3 and y = 2x + 5.

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

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Q: Find the area of the region bounded by the curves 1 y = (x+6)²¹ Y = 4 and the x-axis using vertical…

A: Given problem is :

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

A: Given: Bounded by the curve.y=1-x2And the lines x=-1 and x=2

Q: Sketch the region bounded by the graphs of the equations y = x2 − 1, y = −x + 2, x = 0, x = 1 and…

A: Sketch the region bounded by the graphs of the equations y=x2-1,y=-x+2,x=0,x=1 as shown below.

Q: Find the area of the region bounded by the curves y = 1 (x+4)²² y = 4 and the x-axis using vertical…

A: Draw the region. Find the intersection point and then set up the required double integral to find…

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

A: the area is given by A=∫ab|fx-gx|dx here we have fx=7x g(x)=0 a=0, b=16

Q: Sketch the region bounded by the curves x = 3y2 and x = 12y - y2 - 5 aand find its area.

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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: Sketch the region enclosed by the curves and find its area. 1 y = 6x² ,y = 6/x, x =-andx = 1 Enter…

A: The region enclosed by the curves,y=6x2, y=6x, x=14, x=1

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ į, y = = 4 and the x-axis using…

A: Explanation of the answer is as follows

Q: Sketch the region bounded by the graphs of the equations and find the area of the region. y = 1/x2,…

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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: 2 y = 12 – 3x", y= 4 – x- — х |

A: Let's find.

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

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Q: Sketch the region bounded by the graphs of the equations and find the area of the region. x = y2 −…

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Q: Find the area of the region bounded by the curves 1 y = (x+6)²¹ Y = 4 and the x-axis using vertical…

A: Given

Q: Sketch the region enclosed by the curves and find its area. y = x, y= 4x, y= -x + 4 AREA

A: Topic:- application of integration

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

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Q: Find the area of the region bounded by the curves 1 y = y = 4 and the x-axis using vertical strip.…

A: We have to solve given problems:

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 between the curves 4x + y = 12 and x Area between curves = %3D

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Q: Find the area of the region bounded by the curves y = xe3x-+3 x-axis and the lines x = 0 and x = 1.…

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Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves

A: Solution

Q: Find the enclosed area by the curve with equation y=x^2-9 and x-axis in the region[-1,2]

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Q: Find the area of the region between the curves x 2y and x + y = 1. Area between curves =

A: Given curves are x = 2y2  and x + y = 1 Here we have to find the area between the curves.

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

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Q: Find the area of the region between the curves y = 8 - x2, y = x², x = -3, and x = 3. Area between…

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Q: Sketch the entire region bounded between the curves, x=y^2 and y^2 =x-4. Determine their…

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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 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 curves y = x 2 − 3x + 5 and y = 3x + 5.

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Q: Find the area of the region bounded by y=2x2 -3x+2 the x axis and the vertical lines x=0 and x=2

A: Given that a equation y(x) and we find area bounded by x=0 ,  x= 2  . Here i attached solution of…

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 enclosed by the curves defined by  y=x2-2x-2 and y-x+8

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Q: Find the area of the region between the curves y = x² and y = x. Area between curves =

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Sketch the region bounded by x= 4– y² and x- y=-2. Find the area of the bounded region

A: Given:x=4-y2,x-y=-2

Q: Find the area of the region between the curves 4x + y = 12 and x = y. |3D Area between curves =

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Q: Find the area of the region bounded by the curves 1 y= (x+6)²¹ y = 4 and the x-axis using vertical…

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Q: find the total area between the region y=3x^2-3, -2< x < 2 and the x axis

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Q: 48. Bounded by the curve y = 2/, the æ-axis, and the lines æ = 0 and æ = 16

A: Area under curve

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

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Q: 2 x = 8 – y, x=y¯ - 8 ?, x =y² - 8

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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.