Find the area bounded between curves: (show the figure with the rectangular strip used)   x = y^2 – 2y and x = 4y – y^2

Q: Find the area of the region between the curve y 4 In x and the horizontal axis for

A: We have to find the area of the region between the curve  y=4 ln x and the horizontal axis for…

Q: Sketch the region enclosed by the curves and find its area. y = x, y=3x, y= -x + 2 AREA =

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

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Q: What is the area of the region enclosed by the curve y=x(x-1) (x-2) and the x-axis?

A: Given:            Curve: y=xx-1x-2             Area =∫01xx-1x-2 dx+-1∫12xx-1x-2 dx…

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 curves 1 y y = 4 and the x-axis using vertical strip.…

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

Q: Consider the area of the region bounded by the curves y = 2x +1; x+ y = 7 andx 8. Find y.

A: Formula: The area between the curves y=f(x) and y=g(x) on an interval [a, b] is given by,…

Q: Find the exact area between the curves y =x´ and y = 2 - x. %3D

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Q: Find the area bounded between curves: (show the figure with the rectangular strip used)   y = 6x…

A: First, find the intersection points of the curve y=6x-x2 and y=0. Put y=0 in y=6x-x2 to find the…

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

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y…

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

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Q: Determine the area bounded by the curves y = -x² – 18x + 63 and y = (x – 3)². |

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

A: Given problem is :

Q: Find the area of the region bounded by the curves y = the x-axis using vertical strip. (x+1)2 y = 4…

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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 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 bounded by the curve y²=9x and its latus rectum

A: Given equation is y2=9x the equation of parabola is of the form  y2=4axlatus rectum x=a  and…

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: Sketch the region enclosed by the curves and find its area. y = 9r° ,y = 9/ñx = andx = 1 = 9Vã.x…

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

A: Explanation of the answer is as follows

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

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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 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: Sketch the region enclosed by the curves and find its area. y = x, y = 2x, y= -x + 4 AREA =

A: The region is bounded by y=x, y=2x, y=-x+4

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 bounded by the curves: y = 5x y = 5/x Area = Check

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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 region bounded by the curves 1 y=. (x+8)2¹ , y = 4 and the x-axis using…

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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 bounded by the curves y = x2 and x2 + y = 4x.

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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 the region bounded by the curves y = x 2 − 3x + 5 and y = 3x + 5.

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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 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: Find the area bounded by the given curves. Use vertical strip x² = y - 1 and x = y - 3

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Q: Determine the area bounded by the curves Y = -x² – 18x + 88 and y = (x – 4)².

A: To determine the area bounded by the curves

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 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 area of the region bounded by the curves y = (x+8)2 y = 4 and the x-axis using vertical…

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Q: Find the area bounded by the curve x = ý +2y and the line x = 3.Use horizontal strip.

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Q: Sketch the region enclosed by the curves and find its area. y = x, y = 5x, y = -x +4 AREA =

A: Given that     y = x , y = 5x , y = -x+4 .

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.