48. Bounded by the curve y = 2/, the æ-axis, and the lines æ = 0 and æ = 16

Q: Find the area enclosed by the x-axis  and the curve x = 1 + et y=  t - t 2

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Q: Find the exact area of the region that lies under the curve given by y = 10/2x +1, 0<x <1 %3D

A: We know the area of the region that lies under the curve  y=f(x),  a≤x≤b is given by Area =∫aby dx…

Q: 3 a. y= 2x and y =8– 4x b. y= x°, y =8, and x= 0

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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 enclosed by the curve y=(x)^1/2, the tangent to the curve at x=4 and y axis.

A: Consider the provided information, y=x12 The tangent to the curve at x=4 and y axis. Find the area…

Q: Sketch the region bounded by the curves x = Vy+ 8 , x = y – 4 and evaluate the area.

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Q: Find the area of the region enclosed by the line y=4 and the curves y=e^x and y=(x-1)^2

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Q: Determine the area of the region between the following curve. x = |y| and 2x = −y^2 + 2

A: Given that, x = |y| and 2x = −y2 + 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.

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Q: Find the area between the curves y = x2− 6 and y = x/2 − 3. Convert a and b to decimals

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Q: Find the area of the region in the first quadrant bounded on the left by the​ y-axis, below by the…

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Q: Find the area between the curves.

A: Given: The curves are y =x and y =xx  .

Q: 2) Find the area between the curve y ? = 2x – 5 and the line y = x – 4.

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Q: Find the area of the region between the curves y = 1+ Væ and y = (3 + x)/3. Area between curves =

A: Firstly we find out the points of intersection, we put equation equal to each other , 1+x = 3+x/3 1…

Q: Find the total area of the region between the curve and the x-axis. 2) y = (x + 1/x; 4 sx s 9

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Q: Determine the area (in units) of the region between the two curves by integrating over the x-axis. y…

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Q: Find the area of the region cut from the first quadrant by the curve x1/2 + y1/2 = a1/2.

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Q: A// Find the area of the region bounded above by (y= e), bounded below by (y x)and the boundary line…

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Q: Graph the equations and shade the area of the region between the curves y = x3 and y = x2 − 7x over…

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Q: 3. Find the area of the region bounded by the curves y = 1 (x+1)2/ the x-axis using vertical strip.…

A: Solution :

Q: Find the area of the region between the curves (x = y² ) and (x = y + 2 ) in the first quadrant.

A: The formula to find the area under the region between the curves is Area=∫y=ay=b[f1(y)-f2(y)]dy.…

Q: Find the total area of the region between the curve and the x-axis. y = 2x +7;1sxs5 O 26 O 52 O 18 O…

A: Given query is to find total area of region bound by the curve with x axis.

Q: Find the total area of the region between the curve and the x-axis. y= 2x-x, 0sx s2 O A. 3 O B. 3.…

A: Explanation: Given that: y=2x-x2 Concept: The area under the curve  A=∫abfxdx here a=0b=2

Q: Find the area of the region that is enclosed between the curves y = x² and y = x + 6.

A: The given curves are, y=x2 and y=x+6. The objective is to find the area of the region that is…

Q: Find the area bounded by the given curves. y = 8x3 + 7 and y = 8x + 7 _________ square units

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Q: Find the area between the curves y= 7cos(2x) , y= 7sin(4x), x=0, x=pi/4

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

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Q: Find the area between the curve inclosed by the curve x = 2y^2 and the curve x = 4 + y^2

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

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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.…

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Q: Find the area enclosed by the curve x = t – 2t, y = vt and the y-axis |

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Q: 2 y = x - 3x, y=x 3r.

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Q: Find the area bounded by the curve y = 7x In(x), the x-axis, and the lines x = 1 and x = e.

A: Given:y=7xlnxlines x=1 and x=eTo find:Area A=??

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: Find the area enclosed between the x-axis and the curve y = (x+ 3)²,0 < x < 1.

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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 between the curves y=Vx and y x for

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Q: Find the total area of the region between the curve and the x-axis. 7) y = 2x - x2; 0 sx<2

A: Given, The curve  y = 2x-x2   ;  0≤x≤2 We have to find the area of region between the curve and the…

Q: Find the total area of the region between the curve and the x-axis 1 xs3 4 ОА. 3 O A. OB. В. О С. 3…

A: *to find:- total area.

Q: Find the area of the region bounded by the curve y = ln x, the x axis, and the line x = e^2

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Q: Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

A: Given data: The given equation of the line is y=x/4. The first equation of the curve is y=1+x1/2.…

Q: Graph the region between the curves and use your calculatorto compute the area correct to five…

A: The equations given are , y=21+x4 , y=x2. The region bounded by these curves is shown by the…

Q: Find the area enclosed between the line y 1 and the curve y = x2 – 4x + 4.

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Q: Determine the area of the given region under the curve. y = y 2.

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Q: Find the area between the curve and the x axis over the indicated interval. Y=4-x square; [-2,2|

A: Given: Y=4-x2 to find out: area between the curve and the x -axis over the interval [-2,2]

Q: Find the volume of the area bounded by the curve y²=12x and the line x=3 revolved about x=3

A: Finding the volume of solid generated by given curve

Q: 4. Find the area enclosed by the curve: x=t2 – 2t, y= vt and the y-axis

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Q: Find the area of the region between the curves y = x and y Vx. Area between curves =

A: Find the intersection point and identify which curve is above and which curve is below and then find…

Q: Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

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Q: Find the area enclosed between the X-axis and the curve y = (x +1)°,0 < a < 3.

A: The area under a curve is the area between a curve fx and the x-axis on an interval a, b given…

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.