Find the area bounded by the given curve and line. Show your solution below 1. y = x^2 + 3 and y = 7 2. y = 2x^2 and y = 4x + 6 3. y = -x^2 + 4x and y = x^2 4. y = x^3 - 6x^2 + 8x and y = x^2 - 4x

Q: Find the area bounded by the parabola y^2=4x and the line 2x-4. (with graph)

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Q: Find the area bounded by the parabola y2 − 3x + 3 = 0 and the line x = 4. With illustrations please

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Q: By integration, determine the area bounded by the curves y = 6x – x ^2and y = x^2 – 2x.

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Q: y= -x² + 9; 0 sxs5 x< + 9; 0 < x< 5

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Q: Estimate the area between the curve y = x^2 - 2x + 5 and the x-axis between x = 0 and x = 3 using 6…

A: Given, y=x2-2x+5 Here, a=0, b=3 and n=6 Therefore, ∆x=b-an3-06=12=0.5 Therefore the intervals are,…

Q: Find the area between the curves. x = 1, x = 2, y = 3x3 + 2, y = 0

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Q: Find the area bounded by the curve y=4x-x? and the lines x=-2 and y=4.

A: The given equation forms a downward parabola.

Q: Find the area of the region bounded by the graphs of the equations.              y = 5x2 + 2,    x =…

A: Given  The equation  is  y = 5x2 + 2,    x = 0,   x = 2,    y = 0 Formula for area under the curve…

Q: Find the area bounded by the indicated curves. y = x4 - 18x? + 81, y = 81 - x

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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 bounded by the curve: y = 8x – x² and y = 3x

A: a) Consider

Q: Find the area between the curve y = 4 – x² and the line y = -x + 2.

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Q: Find the area between the curves. x = -2, x = 1, y = 2x, y = x2 - 3

A: Given curves,  y = 2x y = x2 - 3 x = -2 x = 1 To find the area enclosed.

Q: What is the area bounded by the curves y2= 6x and x2 = 6y?

A: topic - area bounded by curves

Q: Find the area bounded by the curve 2x2 + 4x + y – 0 and the line y + x = 0

A: To find the area of region bounded by the given curves.

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

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Q: Find the area bounded by the curves y= 5x and y = 15x.

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Q: Find the area of the region bounded by y = 3x + 10, y = -4x + 1 and x = 12. Leave your answer…

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Q: Find the area of the region bounded by the graphs of the equations. y = 5x2 + 3, x = 0, x = 2, y = 0

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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 bounded by the give curves y=6x2-8x-2 and y= 3x2+4x-11

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Q: Determine the area bounded by the curve y = 2x - x^2 + 5 and the line joining the points (3,2) and…

A: Please see the explanation below

Q: Find the area between the curves -4x + y = 16 and -2x2 = -y+ 10.

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Q: Solve the area bounded by the curve (x – 2)2 = – ( y – 4) and the lines x = – 2 and y = 4.

A: We need to find the area bounded by the curve (x – 2)2 = – ( y – 4) and the lines x = – 2 and y = 4.…

Q: Calculate the area between the curves y = 7- 2x2, y = x2 + 4, and the x-axis.

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Q: Solve the area bounded by the curve x=y^2 and the line y=x+1, y=2, and y=-2. Graph manually.

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Q: Find the area between the curve x = y2 and the line x = y + 2 Solution : * with respect to x:

A: Given curves x=y2. . . . 1x=y+2. . . . .2 Equating (1) and (2) y2=y+2y2-y-2=0y-2y+1=0y=2,-1

Q: Find the area between the curves y = x2 - 8 and y = 4 - x.

A: Explanation of the answer is as follows

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 between the curves: y=x^3−10x^2+21xx and y=−x^3+10x^2−21x

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Q: The area bounded by the curve y = 6x and the lines x = 7,x = 11 and x – axis ахis is

A: → y = mx is the equation of straight line passing through origin with slope m.→ Area of triangle =…

Q: Find the area between the curves. x = - 2 , x = 1 , y = 3x , y = x 2 - 4.

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Q: find the area between the two curvesx=2-y^2x=y^4

A: Given thatx = 2-y2         ...(1)x = y4            ...(2)

Q: find the area bounded by the curve y=9-x^2 and the x-axis

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Q: 5. x-y(2-y) and x=-y

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

Q: Find the area between the curves y = 4x° and y= 3x + 1.

A: Given the curves y=4x2 and curve y=3x+1. We need to find the area between two curves.

Q: Find the area bounded by the given curves, axes and/or lines. 1. у2 +х — 4у 3 5; у-ахis 2. y = 3x –…

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Q: Calculate the area described by the equation y= -6x² +24x + 10, bounded by the lines x = 0 and x =…

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Q: Find the area bounded by the indicated curves. y=7-7x2, y 0

A: We have to find out the area enclosed by the curves

Q: Find the area between the curves. y=x² - 23, y = 9 – 4x

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Q: Find the area of the region in the first quadrant bounded by the line y=3​x, the line x=4​, the…

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Q: Find the area between the curves -16 = 4x- y and -10 = 2x-y.

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Q: Find the area bounded by the curve x²=y+2 and the line x+y=0

A: Integrals and derivatives are considered as the inverses of each other. For example If we integrate…

Q: Find the area between the curves. 3x 3x x-0, x-D4, y3D2e" y-e

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Q: Find the area of the region bounded by y = 7x + 7, y = -9x + 4 and x = 15. Leave your answer correct…

A: The solution of the problem is given in the next steps.

Q: Find the area bounded by the given curves. y = 4x3 + 5 and y = 4x + 5        square units

A: We first sketch the area using a graphing calculator  There are two areas. They are symmetric. So…

Q: What is the area bounded by the curve y^2=x and the line x-4=0?

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Q: Find the area bounded by the curves, 2x² + 4x + y =0 and y = 2x.

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Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.  Show full complete solution.

A: Given : Curve : y²= 4x              and line  2x+y=4 To find : Area between the curve and line

Q: Find the area of the region bounded by y = 4x + 6, y = -3x +1 and x = 15. Leave your answer correct…

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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.