2 1 y ==x = - eğrisinin 1sx< 2 3 2

Q: Find the area of the surface generated when the given curve is revolved about the given axis. x3 y=…

A: If the curve y=fx, a≤x≤b is revolved about   x-axis then surface area is given by  A=2π∫ab  fx…

Q: Find the area of the surface generated when the given curve is revolved about the given axis. 1 3 y=…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: AJKL undergoes a dilation centered at the origin. The result is AJ'K'L'. Which rule describes the…

A: ∆JKL undergoes a dilation centred at the origin.We know that the scale of dilation is the ratio of…

Q: Find the area of the surface generated by revolving x= 21-y,0sys about the y-axis. x=2 The area is…

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Q: Find the area of the region enclosed by the curves. y= \x? - 9| and y = +9 2 The area is (Simplify…

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Q: Find the area of the region enclosed by the curves y and y = 3 %3D 1+ 25 The area of the region…

A: We will solve the problem.

Q: How much larger does a figure get after the dilation D:(x, y) = (2.5x, 2.5y) is performed on it?…

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Q: Find the surface area of revolution about the x-axis of y = 5x + 6 over the interval 1 Next…

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Q: Q5 Find the lateral surface area of the cone generated by revolving the line segment 5x – 8y + 40 =…

A: Given a equation of line-                                         5x-8y+40 = 0. We have to find- a)…

Q: 135 135 Find the area of the surface generated by revolving x= 4/9-y, 0sys about the y-axis. 16 16…

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Q: Find the area of the surface generated by revolving x= 4/1-y, 0sys6 about the y-axis. :16 16 x-4/T-…

A: Given x=41-y ,0≤y≤716

Q: They want it the format of something like this  8pie(45^2/3 - 27^2/3)

A: The curve which is revolved around y-axis is given as .

Q: Find the area of the region bounded by the spiral r= 90 for 0s0ST. r= 90 2 (9x, 1) The area is (Type…

A: Two common coordinate systems used to represent a point in the plane are the cartesian coordinate…

Q: Q5 Find the lateral surface area of the cone generated by revolving the line segment 5x – 8y + 40 =…

A: Definition used -        The lateral surface area of the cone generating by revolving the line…

Q: Identify the expression below that represents the volume of the solid obtained by rotating about the…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y= for…

A: We know that area of surface obtained by rotating y=f(x) from x=a to x=b  about x-axis is

Q: Find the area of the surface generated when the given curve is revolved about the given axis. 1 27…

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Q: Q4: Solve A OR B A) Find the volume of the region cut from the cylinder x' + y 4 by the plane Z= 0…

A: #a Find the volume

Q: The figure shows the surface created when the cylinder y² + z? = 7 intersects the cylinder x² + z? =…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y=4/x,…

A: Area problem....

Q: 135 135 Find the area of the surface generated by revolving x= 49-y,0sys about the y-axis. 16…

A: Consider the given: x=49−yLimits 0≤y≤13516dxdy=−29−y Find the surface area:…

Q: Find the area od the surface generated by revolving the curve y=2√x  1<=x<=2 about x-axis

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Q: (a) y² + ² = 4 that lies inside the cylinder x² + y² = 3. Find the area of the surface S, which is…

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Q: 63 Find the area of the surface generated by revolving x= 4/4-y, 0sys about the y-axis. x=4/4-y

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Q: Find the area of the surface generated by revolving x = 2/4-y , 0sys3 about the y-axis. 3. (2,3)…

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Q: Find the surface area of the trapezoidal prism below. Do not include units in your answer. Round…

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Q: Find e > 0 such that the area of the region enclosed by the parabolas y = a? – c² and y = c² – a² is…

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Q: Find the area of the region enclosed by the curves. y = |x? - 36| and y = d%3D 9 + 36 The area is…

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Q: Find the volume of the solid that results when the region enclosed by 1 -x² and x = 49 the curves y…

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Q: x² + y² that lies between the cylinders x? + y² = 1 Find the area of the part of the cone z = x² +…

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Q: 5. Find the surface area of the part of the paraboloid y = 5– x² – 2² that lies inside the cylinder…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y =…

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Q: 4. Find the surface area of the cone shown. Round your answer to two decimal places. 9 cm 2 cm…

A: As per guideline we will find the solution of question number 4 in the following step. If you need…

Q: 39. The curve has an equation of x² + y2 = 25. The area on the first quadrant of the curve is…

A: Given curve x^2+y^2=25.

Q: Find the area of the surface generated by revolving x = /18y - y? on the interval 3sys 17 about the…

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Q: The frustum below is made by horizontally slicing off the top of a right cone. What is the total…

A: The total surface area of the frustum is given by: TSA=π(x+y)(I)+πx2+y2 where I=z2+(x-y)2

Q: Solution with important notes y = x? 3. Find the center of mass of thin plate For the shaded region…

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Q: calc 3 Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 81, above the…

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Q: Find the surface area of revolution about the x-axis of y = 6 sin(6x) over the interval 0 < a <…

A: Find the surface area of revolution

Q: 1. Let a be a positive number. Find the surface area of the solid obtained by revolving the curve…

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Q: Find the area of the surface generated by revolving x = / 12y-y on the interval 4 sys6 about the…

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Q: Find the surface area of the solid that is obtained by rotating the graph of y = f (x) about the…

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Q: The surface area of the surface generated by revolving y=x³ , 0<x<1 about the x- axis is S×3.56312…

A: Option 2 none

Q: an exercise ball is inflated, its radius increases from 30cm to 31cm. Using Linear Approximation,…

A: Here we need to find the change in volume of the sphere. The equation for finding volume of a sphere…

Q: Find the area of the region between the parabola y=64 - x² and the x-axis. Round your answer to…

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Q: b) The diagram below shows a solid shape E with uniform cross-section. Find its volume. '10 cm! 12…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y = 2x…

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Q: y3 Find the surface area of the object obtained by rotating x = + 1< y<4 about the y-axis. 12 y

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y =…

A: Consider the curves, y=4x  ,   5≤x≤77 The area of the surface generated when the graph of function…

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.