Sketch the region enclosed by y = esz, y = e², and a = 1. Find the area of the region.

Q: sketch the region enclosed by the carves and find its area X Sy + 1a = .....

A: The detailed solution is explained in steps 2 and 3.  First we have to sketch the curves and then…

Q: Find the the surface area of of the indicated surface The portion x +3y+z = 6 in the first octant.

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Q: Sketch the region between y = sin (x) and y = 0 for a between 0 and T. As well, find the area of…

A: NOTE: Refresh your page if you can't see any equations. . here we have the lower and upper limit…

Q: the region R-that lies inside the Cardioid Y=1+ Cose and outside the Circle r=1

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Q: Find the area of the shaded region. r = Vē 9n?

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Q: y = 2Vx, y= Find the area of the region enclosed by the curves.

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Q: Sketch and find the area of the region lies inside the cardioid (r = 1+ cose) and outside the circle…

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Q: Sketch the region enclosed by y = 7x and y = 3x". Find the area of the region.

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Q: Find the area of the shaded region : y = sec? x 2+ y = cos x 4 2

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Q: Find the area bounded by the given curves and lines. 1 y? (2–æ)³ 3

A: We have to find area

Q: Find the area of the shaded region. 44) 2) (II/4, 2) TE: II II 2 311 4 y = 2 y = csc²x X

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Q: Find the area of the shaded region.

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Q: Find the total area of the curve r=2sinA+2cosA.

A: We have to find the total area of the given curve.

Q: Sketch the region enclosed by y = 2x and y 7x. Find the area of the region.

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Q: Sketch the region enclosed by the given curves. y = 8x, y =x, y = 2/x, У 6F 6F 4 1 4 У 3 3 1 3 4…

A: First of all, plot the curves y = 2/x, y = 8x and y = (1/8) x using the graphing utility.Consider…

Q: 1. Find the area of the region between y = a2 and y = -a? + 18z.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find the area of the region R enclosed by the parabola y = x² and the line y = x +2. Solution:

A: " Since you have asked two questions, we will solve the first question for you, if you want second…

Q: Determine the area of the region bounded by æ = y? – y – 6 and a = 2y+ 4.

A: Area between two carves = double integration of (dx dy) From given two carves we will find limits of…

Q: Find the area of the shaded region: 1. yA x= 2 2, 4) y= x? y= 0

A: We will find the area of shaded region as following.

Q: 10z Sketch the region enclosed by y = 5, y = el, and a = 1. Find the area of the region.

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Q: Determine the area of the region L X-axis and y-axis in the first quadrant.

A: The area between the curves y=1+x and y=3-x on interval 0, 3:

Q: Find the area of the region enclosed by y = 3.25x and x = 7 – y?. 4 5 Use horizontal strips to find…

A: Given, The curves y = 3.25x  and x = 7-y2  We have to find the area of the enclosed region using…

Q: 2. Find the area of the region enclosed by æ + y? = 0 and ¤+3y² = 2.

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Q: Find the area between y= e" and y = e over [0, 1]. %3D A =

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Q: Find the area of the shaded region 14 LA bounded above by y = 2, bounded b TE lo 1)

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Q: Sketch the region enclosed by y = e, y = e, and z = 1. Find the area of the region. Question Help: D…

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Q: The area of the region enclosed by y = 49(x + 1)ez, y = 49e7z, x = 1 and x = 12 is

A: Solution is given below :

Q: Sketch and find the area of the region lies inside the cardioid (r = 1+ cose and outside the circle…

A: Find the intersection of the curves by comparing the RHS of the equations r=1+cosθ and r=3cosθ to…

Q: Find the area of the region enclosed by the curves y = x2 – 4 and y = 5. The area of the region…

A: area of the region enclosed by the curve is 36 detailed solution is given below

Q: Find the area of the region between the following curves by integrating with respect to y. If…

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Q: Find the area enclosed by the curve r= 5cos0

A: The given curve is as follows:r=5cosθTo find the area enclosed by the curve r=5cosθ

Q: Find the area of the shaded region    y = - 1  ,  y = 1            ,  x  = e y   , x = y 2  - 2

A: x=ey,  x=y2-2, y=-1  & y=1. The graph is,

Q: Sketch the region enclosed by y = e, y = et, and a = 1. Find the area of the region. %3D Question…

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Q: Sketch the region A={(x, y)|(y< log, x)n ys s}.

A: Explained below

Q: Sketch the region enclosed by y = e, y = e, and a 1. Find the area of the region.

A: we have given y=e4x ,y=e8x and x=1 the region of of given functions are

Q: Find the area enclosed by the given curve r=2acos20

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Q: Find the area of the region enclosed by the curves y = 2 - x² and y = x. (a) (c) 9 2 54 (b) (d) 40 7…

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Q: Sketch

A: Please refer to the image below

Q: 2. Find the area of the region bounded by y = VI and y = r.

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Q: Find the area of the region in the 1st quadrant bounded by y = x2 + 1, y = 1 – x², and x = 1.

A: Given the curves and lines y=x2+1, y=1-x2 and x=1 The figure of an area of the following region is…

Q: Sketch the region enclosed between graphs y = Vx and 1 y = – and x = 8. [Hint: you need to find the…

A: Solved below

Q: Find the area of the following regions. The region enclosed by the curves y = 2x and y = x². а. b.…

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Q: Find the area of the region that lies inside both curves.

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Q: Find the area of the shaded region. y = x3 - 4x (3,15) C0,0) 3 33 O A.

A: The objective is to find the area of shaded region

Q: Sketch the region enclosed by y RV-eand r-1. Find the area of the region.

A: Region is bounded by the given curve y=e2x , y=e7x  and  x=1

Q: Find the area enclosed by the given curves y = 12x? – 3 and y = 7 cos(Tx). You may find it useful to…

A: Given functions are y=12x2-3 and y=7 cosπx

Q: Sketch and find the area of the region lies inside the cardioid (r = 1 + coso) and outside the…

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Q: Sketch the region enclosed by y 6x and y = x. Then find the area of the region.

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Q: Find the area of the region that lies inside the first curve and outside the second curve. r =…

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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.