Sketch the region bounded by the curves y = vx + 4 , y=x +2 and evaluate the area.

Q: Find the area of the region bounded by the line y=x, x=2 and by the curve y= (1/x2)

A: Area of the region shaded below÷

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 three curves y = x^2 , y = 8−x^2 , and 4x−y + 12 = 0.

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Q: Sketch the region enclosed by the curves x-6=3y and x-24=(y-6)^2 and compute the area.

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Q: Sketch the region bounded by the curves 4x2 + y = 28 and x* – y = 4, then find the area of the…

A: Area between curves

Q: Determine the area of the region between the two curves by integrating over .the y-axis X = y2 and x…

A: Area of the region between the two curves x1(y)  and  x2(y) is given by ∫abx1-x2dy    where a≤y≤b

Q: Find the area bounded by the curves y = 3 Vx +1 and y = + 1. %3D

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Q: Find the area of the region R bounded by y-3-x and coordinate axes.

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Q: Sketch the region enclosed by the curves and find its area. y = 7x2 .y = 7 Vx,x = 1 and x = Enter…

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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 area of the region bounded by y= Vx+1 and y = x – 2x – 3. %3D

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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: Sketch the region bounded by the given curves, then find its area. y = 12 - 3x^2, y = 4 - x^2

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Q: What is the area of the region bounded by the y axis with lines?

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Q: Sketch the region by the curves and find its area. y=x^2 y=x+2

A: Given,

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 bounded by y =2x and y = 9x - x2. Sketch the region.

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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 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: What is the area of the region enclosed by the curve y=x^2 and the lines y=x+6, x=0 and x=5?

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Q: Sketch the region bounded by the curves y = /x and y = x/3 and find the area of the region.

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Q: Calculate the area of a region bounded by the curves =x and y= Vx

A: I am solving this in step 2

Q: Sketch the region bounded by the curves y = vx – 2 , y = x – 4 and evaluate the area

A: Solve by integration

Q: 16. y= Vx, y= %3D

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

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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 bounded by the curves 1 y = (x+6)²¹ Y = 4 and the x-axis using vertical…

A: Given

Q: Find the area of the region enclosed by the curves x = 4, y = 1, y = Vx – 4.

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find the area bounded by the curves x 2 = y − 1 and = y − 3 .

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Q: Sketch the region enclosed by the curves/lines x = y, y =1/x, x = 3 and find its area.

A: given,         x=yy=1/xx=3

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 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: What is the area of the region enclosed by the curve y=e^x and the lines x=-1 and y=3?

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Q: Compute the area of the region bounded by the curves y = Vx and y = x

A: ANSWER:

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 enclosed by the curves y=x'and y = 4x. (Show clear work!

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Q: | = x – 2 and y =

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Q: Find the area of the region enclosed by the curves between their intersections. y = 4x2 and y = Vx

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Q: Find the area of the region in the first quadrant that is enclosed by the curves x=y, y=x-, and the…

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Q: sketch the region enclosed by the curves and find its area y=1/x, y=2x-1,y=9

A: Consider the following graph:

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 = 6 – x² and y = x + 4.

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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 the curves 1 y= (x+6)²¹ y = 4 and the x-axis using vertical…

A:

Q: Sketch the region enclosed by y = 4x and y= 6x². Decide whether to integrate with respect to x or y.…

A: Given query is to find area under the curve.

Q: Sketch the region bounded by the curves 5x2 +y = 31 and x – y = 5, then find the area of the region.…

A: The solution are next step

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: Sketch the region enclosed by x+y^2=6 and x+y=0. Decide whether to integrate with respect to x or y,…

A: We first graph the given equations. They intersect at (-3,3) and (2,-2)

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.