Sketch the region enclosed by the given curves andfind its area.    y =  e x   ,  y = x e x     , x = 0

Q: Find the value of k such that the area of the region under the curve y = x(k – x), (0 < x < k), is 1…

A: Given: To find the value of k such that the area of the region under the curve y=x(k-x), (0≤x≤k) is…

Q: Help please

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Q: Find the area of the region bounded by the curves y = x, x = 1 and y = 0. %3D A. 1 В. C. 1 3 D. 1 4…

A: Area = integration of upper curve - lower curve and put the limits.

Q: Find the area bounded by the curve ay = x² and the lines y = a and y = 4a.

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Q: Exercises: Sketch the region bounded by the given curves, then find its area. 1. y = x², y = 2x

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Sketch the region enclosed by the given curves. x = 9y, x = 4 + 5y? y y 1.0 8 . 0.5 8. -0.5 -0.5…

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Q: Find the area of region enclosed by x = t – ť², y = t – t", 0 <t < 1 using Green's Theorem.

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r…

A: The area under the curve γ=fθ such that α≤θ≤β is given by the formula A=12∫αβf(θ)2dθ. The given…

Q: Sketch the bounded region enclosed by y=e^5x, y=e^6x and x=1. Decide whether to integrate with…

A: Sketch the bounded region enclosed by y=e^5x, y=e^6x and x=1. Decide whether to integrate with…

Q: Find the area of the region bounded by the given curve: x=e, y=0, y=1/x, y=x2

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Q: Sketch the region enclosed by the given curves and find its area. y= cosx, y= (1-2x)/pi

A: y=cosx  &amp;  y=1-2xπ The region enclosed by these curves is,

Q: Find the area enclosed between the curve y = cos? x and the line y = 1: %3D Y= cosr

A: Here we have to find the area of the bounded region between the curve y=cos2x and the line y=1

Q: Sketch the region enclosed by y=e^3x ,y=e^8x, and x=1. Decide whether to integrate with respect to x…

A: The given two curves and horizontal line

Q: Find the area enclosed by the given curves. y =x, y= 4x O A. 16 O B. 2 O C. 8 O D. 4

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Q: Given that R is the region bounded by the curve y = x+3 and line y= x-3. (a) Sketch the region R.

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Q: Find the area of the region bound by the following curves: y = /x, y= 6 – x, y = 1. O 17/6 O 1/2 O…

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Q: ind the area of the region bounded between the curves (make sure you draw the picture). -2x =) y =…

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Q: Evaluate SSA, dA, where R is the region bounded by y=x2 and x = y² in the first quadrant. X

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Q: Let R be the region enclosed between the curves r²=y-1 and y=5. Sketch R and find its area.

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Q: Find the areas enclosed by the following curves: (c) y = xv1 – x², and y = 0 |

A: The area enclosed by the curves y=x1-x2, y=0. So, area enclosed by the region is: A1=∫-10∫0x1-x2dy…

Q: 1. Sketch the region enclosed by the given curves and find its area. y = x?, y = x*

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. Зп…

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Q: x = sin y, x = 0, y = 7/4, y = 3/4 %3D

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Q: Find the area of the region bounded by the given curves. y = sin?(x), y = sin°(x), o SXST

A: y=sin2x, y=sin3x,   0≤x≤π Now the diagrammatic representation of the area is,

Q: Sketch the region enclosed by the given curves. y = Vx, y = X = 25 y 6 6 4 2 X 10 15 20 25 10 15 20…

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Q: Find the area of the region enclosed by the given curves. y = sin x, y = 2x/T, x > 0

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

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Q: Sketch the bounded region enclosed by y=e^4x,y=e^9x and x=1. Decide whether to integrate with…

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Q: Find the area enclosed by the given curves. y = csc 2 x, y = cot 2 x, » 7, and x = 00

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Q: Find the area enclosed by the given curves. y = x°, y = 4x 4. O 16 2 8.

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Q: Find the area of the region bounded by the given curves. a. y = 2 – x2, y = x² b. у%3D Зх + 2, у %3D…

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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: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

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Q: Find the area of the region bounded by the curves y + 2 = Vx and y = x-2 O a. Ob. 5 9. 1

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Q: Find the area oF the regioN eNclosed between the curves de Fived by the equations y =Vx +2, y: x,…

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Q: y = e", y = xe and x = 0

A: The region bounded by the given curve is:

Q: Sketch the region enclosed by the given curves. y =- y = 8x, y = x > 0 y y 6 4 3 3 2 1 1 X 2 4 -1 3…

A: Given that the curves are      y=2/x , y=8x , y=x/8 , x&gt;0 Here we have to sketch the region and…

Q: 343 2 1. y = x² - 9 and y = x + 3 (Answer: 6 s. u.)

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Q: Find the area of the plane region bounded by the given curves: y= x, y= 2x, and x+y= 6

A: Given: y=x, y=2x and x+y=6 Now find the point of intersection between the line y=x &amp; x+y=6…

Q: Find the area of the region bounded by the given curve: r = 5e° 6. on the interval 5"

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Q: Find the area of the region enclosed by the curves: y = sin x, y = cos x, x =0, x = 27

A: First draw the figure of y=sin x and y=cos x for the interval 0,2π.The graph is shown below, cosine…

Q: Find the area enclosed by the given curves. y =x, y x2 113 1_6 1의112

A: solve the following

Q: Sketch the region enclosed by y=e^4x, y=e^9x , and x=1x=1. Decide whether to integrate with respect…

A: Given:   y=e^4x, y=e^9x   x = 1

Q: Find the area enclosed by the given curves. 24) y = 1/2 x², y = , y = -x² + 6

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Q: Sketch the region enclosed by 2y=4 sqrt(x), y=3, and 2y+3x=7. Decide whether to integrate with…

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Q: Find the area of the region bounded by the given curves. y = 1/x, y = x2, y = 0, x = e

A: Given curves, y=1x, y=x2, y=0 x=e

Q: Find the area enclosed by the given curves. y=x, y= 4x O A. 8 О В. 2 О с. 16 O D. 4

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Q: Find the area bounded by the given curves. y = x², y = 2x² - 3x A. 9.0 sq. units B. 40 so units CAF

A: We have to find area

Q: y = sin x, y = x, 0 <x < T/4

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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.