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

Q: Determine the approximate area of the sector shown?

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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 area of the region enclosed by one loop of the curve  r= 3cos 40

A: We have to find the area by one loop of the curve r=3cos4θ We know area A=12∫-aar2dθ for cosθ we…

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: Consider the following shaded region. y = ax - x? y=bx Find the area S of this region if a = 6, b =…

A: y = ax-x2   ,   y =bxa=6  ,  b=1y = 6x-x2  , y = x

Q: Find the area of the region inside the circle r=4cos(θ) and outside the circle r=2

A: Given: -

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

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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 = 3x and y = 6x. Find the area of the region.

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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: Sketch the region enclosed by y=4x and y=5x^2. Find the area of that region

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Q: b) Calculate the area of the region.

A: Integrate the given integral with respect to dθ.

Q: Sketch and find the area of the region in the first quadrant outside the circle r=6 and inside…

A: There are two circles. r=6 and r=4+4 cos0=8   Using graphing calculator we draw the graph of both…

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 region Inside the circle r = 6 above the line r = 3 csc u

A: r=6  &  r=3 cscθ On simplification, we get ⇒3 cscθ=6⇒cscθ=2⇒θ=π6,  5π6

Q: Determine the area of the region enclosed by the curves y = 1 + vE, y=3 – z, x-axis and y-axis in…

A: The area is the measure of the amount of space occupied by a plane figure. It is measured in terms…

Q: Calculate the area outside the r=8sinθ curve and inside the r=4+4sinθ curve. Area=?

A: Calculate the area outside the r=8sinθ curve and inside the r=4+4sinθ curve.

Q: d. Find the area between y = x* – x² and y = x2. Sketch the region.

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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: Sketch the region enclosed by y 7x and y = 6x². Find the area of the region.

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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 region in the first quadrant enclosed by y = Vx, y = 2 – x and y = x².

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Q: Sketch the region enclosed by y = 3x and y = 6x°. Find the area of the region.

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Q: Sketch the region A

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Q: Find the area of the region. x) = Sex/s y

A: From the graph we see that, x is from 0 to 1.The given function is f(x)=5ex5

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: 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: Find the area of the region. y? = x°(1 - x²) y 2- -2 2 -2+

A: The question is from the topic of application of Derivatives

Q: Find the area of the region that lies inside the circle r = 3sintheta and outside the cardioid r…

A: In this question we will use the basics of calculus i.e application of integration. First we will…

Q: Sketch the region and find its area (if the area isfinite). S = { ( x, y) |   0<= x < pie /2 ,…

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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: 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 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 region inside the circle r=−6cosθ and outside the circle r=3.

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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: Find the area of the region described in the following The region bounded by y = 2 - IxI and y = x?

A: y=2-x and y=x2 The graph is,

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

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Q: Sketch the region enclosed by y 6x and 4x. Find the area of the region.

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Q: Sketch

A: Please refer to the image below

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

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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: 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 of the shaded region. y = <솔, 2) <2,놀) 1.69 1.25 o 1.39 1.50 1/2

A: Given a shaded region which under the curve y=1x between the points x=12 and x=2. Find the area of…

Q: A° n (B UC)° B.

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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: 2x and y 4x?. Sketch the region enclosed by y Find the area of the region.

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Q: Find the area of the region inside the circle r 6 and above the line %3D r= 3 csc 0.

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Q: Find

A: Here Required probability = P (Z&lt;z) =0.0239

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.