Calculate the total area of the region described. Do not count area beneath the x-axis as negative. bounded by the line y = 2x, the x-axis, and the lines x = 2 and x = 5

Q: Find the area of the region. y = x2 − 3x,  y = 4x

A: First graph the given curves.

Q: Find the area of the region bounded by y=0 and y = -5x + x° 47 42 37 42 57 21 57 42 37 21

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Q: Find the area of the region bounded by 2x and the y-axis using the horizontal strip. 4 12 y² +1

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Q: Find the area of the region enclosed by the given curves y = x^2 y = 32/ x^2 + 4

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Q: Find the area of the region enclosed by x = y and x = 1.

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Q: Find the area of the region enclosed by x + y = 2 and x + y = 0

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Q: Find the total area of the shaded region. 1.5- 1- 0.5- 0 y x=12y³ 6 x=12y² (12,1) 12 18

A: The equation of the curves are: x = 12y3 x = 12y2 The graph of the curves is To evaluate: The area…

Q: Find the area of the region enclosed by: y = x³ and Y = = x4

A: Given curves are  y=x3 and y=x4 Point of intersection of the curves are obtained as follows.…

Q: Determine the area of the region between y = x+2, y = 2* + x and the y axis. ABC ттт Arial 3 (12pt)…

A: Given curves  y= 2x+x  y=x+2

Q: Find the total area of the region enclosed by the curve x = y^(2/3) and the lines x = y and y = -1.

A: To determine the area bounded by the curves.

Q: Find the area of the shaded region. y y = Vx 3 마1, 1) x = 27 1 y = X 5 10 15 25 20 2.

A: The area under the graph can be determined by integration. Let, Boundary points are, x1=1 and…

Q: Find the area of the shaded region. y 3 y = Vx 11, 1) x = 27 1 y = 10 15 20 25 2.

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Q: Evaluate the area of the region bounded below by y = x* and above by y = x.

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Q: Determine the area of the given region. The region bounded by y = x2, y = 2x2 - 4x, and y = 0

A: Given, The curves are y = x2, y = 2x2 - 4x, and y = 0 The graph of the region is as below

Q: Find the total area of the region enclosed by the curve x=y^2/3 and the lines x=y and y=−1.

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Q: Calculate the area of the region bounded by x+y = 4, r + y = 8, x = 0, and I = 5.

A: Given:         Area of region bounded by x+y=4…

Q: By sketching the graphs, find the area of the region bounded by, x = /y,y x + 6 and x = 0

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Q: Determine the area of the region enclosed by x=12y^2−3 and y=x−1

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Q: Find the area of the region enclosed by x = y^2 + 2 and x = 2y+6

A: Please refer to the image below.

Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2 A) 1/3 B) 1/4 © 1/5 D 1/6

A: To find the area enclosed between the two given curves.

Q: Given the curve y = x´ and the lines y = 0 and y = 2 – x Find the area of the region bounded by the…

A: Given

Q: Find the area of the region enclosed by x=y^2 and y=x-2

A: To find the area of the region enclosed by x=y2 and y=x-2

Q: Find the area of the region bounded by the following curves. y  =  x2 + 4x,     y  =  160 − x2

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Q: Find the area of the region enclosed by these graphs and the vertical lines x = 1 and x = 4. X…

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Q: Find the area of the given region.

A: Integration is used to find the area under a curve. So, on integrating the function y=x-x2 from x=0…

Q: Calculate the area of the region that lies under thecurve and above the  x-axis. y =2x - x2

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Q: Sketch the region enclosed by y = /x, y = 0, x = 4 and calculate its area.

A: The region enclosed by y=x , y=0 and x=4 is given by:

Q: Find the total area of the region y%= -x-+ 9;0< x 5 05 6. O 10 6. 10 3 98 3

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Q: Find the total areas of the shaded regions

A: according to given figure areaA of shaded region is given by A=∫01x13-x12dx…

Q: Find the area of the region enclosed by x = y and x = Vy– 6.

A: The graph is shown below:

Q: В. Find the area enclosed by the given curve, the x-axis, and given lines. x²+10, x=1 and x 3 3 4. y…

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Q: Find the area of the region enclosed by the curves y = x + 5, y² = = x, y = −1, and y = 2.

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Q: Calculate the area of the region that lies under thecurve and above the  x-axis. y =1- x2

A: The graphical representation of the area is,

Q: Determine the area of the region enclosed by the curves y=1/x, y=1/x2, and x=9.

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Q: Graph the region bounded by the curves and determine the area of the region. x = y? – 2y; x = 0

A: ANSWER :

Q: Find the total area of the region between the curve and the x-axis. 9) y = (x + 4)3; 0 <x<3

A: The Area Under a curve The area under the curve between two points can be found by a definite…

Q: Find the area of the shaded region. y 4 3 2 1 (1, 1) 2 y = √x y = 4 X 6 X = 8 8 X

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Q: Find the area of the region enclosed by y = 4 – x², y = –x + 2, x = -2, and x = 3.

A: Given: - The region enclosed by y=4-x2, y=-x+2, x=-2 and x=3 To find: - The area of the given region…

Q: Calculate the area of the region bounded by r +y = 4, x +y = 8, x = 0, and I = 5.

A: We use the formula to find area enclosed between two curves.

Q: Find the area of the region bounded by the given y = 4ax, y = 4ax°, a > 0

A: The given curves are  y = 4ax y = 4ax3 Intersection point of both curves 4ax = 4ax3 4ax(x2 - 1) = 0…

Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2

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Q: Find the area of the region enclosed by y = –x² +6, y = x, y = 5x, and x > 0.

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Q: Let R be the region enclose by the graphs of y=lnx, the line x=3, and the x-axis. Calculate the…

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Q: Find the area of the region enclosed by these graphs and the vertical lines x = -1 and x = 0. |…

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Q: Give the area of the region enclosed by y = x2 , x = 2, and x – axis. А. 4 В. 8 C. 8/3 D. 4/3

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Q: etch the region enclosed by y = x²y = √√x,x = 0,x = 1 and find its area.

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Q: Given the curve y = x' and the line y = 2 – x. Find the area of the region bounded by the curve and…

A: Area bounded by the curve y=x2 and the line y=2-x

Q: Determine the area of the region enclosed by y = x² and y = Va.

A: In the given question we have to find the area of the region enclosed by the curve y=x2 and y=x.…

Q: Find the area of the region enclosed by the curves: y =x', and y= 2x-x

A: Consider the curves  y=x2y=2x−x2

Q: Find the area of the region enclosed by x=y³ and x=√y-6

A: Given: x=y3, x=y-6 For finding areaA of the region enclosed by given curves, we draw graph of both…

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.