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

Q: Sketch the curve, y=-x +9. Then, find the area between the curve and the x- - axis over the…

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

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Q: Find the area between the curves. y = x2 - 18, y = x - 6

A: y = x2 - 18, y = x - 6

Q: Find the area between the curves.

A: First sketch the region bounded by the curves x=1,  x=6,  y=1x  and  y=12 as shown below.

Q: What is the area (in square units) bounded by the curve y' =x and the line x- 4=0?

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Q: Find the area between the curves y=3/x, y=12x, y=1/3x, x&gt;0

A: We have to find the area between the curves y=3/x, y=12x, y=1/3x, x&gt;0So, first of all we need to…

Q: Find the area bounded by the given curves. y = 3x2 and y = 27…

A: Given:

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

A: so we have and the other function is

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 between the curves 2x^2+4x+y=0 and y=2x

A: Given that: 2x2+4x+y=0    and   y=2x

Q: Estimate the area under the curve y=64-x^3 between x=0 and x=4. Use four rectangles

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Q: Find the area between the two curves on [2,3]. y = ex y = (1/x)

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Q: Find area between the curves y=17/(9+x^2) and y=13/(1+x^2)

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Q: Find the area of the region between the curves 4x + y^2 = 12 and x =y.

A: 4x+y2=12    and  x=y

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: 4 y = 1 + x4' y = 2x2

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Q: Find the area between the two curves: y = x2 and y = 4x + 5

A: In this question we have to find Area.

Q: Find the area bounded by the pair of curves. y = x² + 4x and y = 4x + 1 square units

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Q: Find the area between the two Curves- y=x, a°y = x³ 3,

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Q: Find the area between the two curves y = x^2 and y = 2x – x^2

A: Given:     To determine: The area between the two curves.

Q: Find the area under the curve y = 3xe for æ > 3. area =

A: Given:The given curve is y=3xe-x and x≥3To find:we have to find the area under the curve

Q: Find the area bounded by the curve y = 4x - x² and and the lines x = 0 and y = 4. %3D Answer:

A: we can find the area between the curve and the lines by integrating the curve function through lines…

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

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Q: By double integration, Find the area between the line y=6-2x, the x-axis and y-axis.

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Q: y = 4 – x2 y = 4 – 4x - -5-

A: Definition used -             The area between two curves f(x) and g(x) -…

Q: Find the area between the curves. x = -2, x = 1, y = 2x2 + 5, y = 0

A: Given, x=-2,x=1,y=2x2+5,y=0

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

A:

Q: Two curves having an equation of 2y² and y = 2x² x = intersect each other. Compute the area between…

A: A detailed solution is given below.

Q: Find the area between the curves.  y = |9x|  ,  y= x^2 - 10

A: First we graph the functions. They cut at (-10,90) and (10,90)Area from x=-10 to x=0 is equal to the…

Q: Find the area between the curves. y = x4/3, y = 2x1/3

A: y = x4/3, y = 2x1/3

Q: the

A: Given curve y^=x and y=√x  Line x-4=0   Find area ?

Q: Find the area bounded by y=2*, y = 2x2, the y - axis and x = 1 Write your final answer in two…

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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: Find the area between the curves x = 10 − y2 and y = x − 8

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Q: Find the area between the curves.

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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 y=2%, y = 2x2, the y - axis and x = 1 Write your final answer in two…

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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 enclosed between the line y 1 and the curve y = x2 – 4x + 4.

A:

Q: Find the area between the curves y = 4x – 3 and y = x². %3D

A: Given data is : y=4x-3     .....1 y=x2      .....2 From equation (1) and (2) ,…

Q: y=9-x2 and ミ-4

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

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Q: Find the area between the two curves y = 3 y = x² – 1 1+ x2'

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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 of the region between the curves 4x + y = 12 and x = y. Area between curves =

A: R

Q: y = 3x2, y = 0 and x 31

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Q: Find the area in the first quadrant bounded by y=4x-x² and the x-axis

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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: Determine the two​ t-values that divide the area under the curve into a middle 1−α area and two…

A: Solution

Q: What is the area between the curves y^2 = 3x and y = x^3 using vertical strip?

A: Given: y2=3x y=x3 Draw the region bounded Consider a rectangular strip of length width dx.

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.