4. Find the area of ​​the surface of the revolution formed by rotating the part of the 4x^2 + y^2= 4 ellipse in the first region about the o-y axis.

Q: 10 Find the area of the surface generated by revolving the region bounded by. ISKSS about the…

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Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 – 3y², and the…

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Q: The line y = 2x and the parabola y = 16x intersect at x= 4. Find by a double integral, the area…

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Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y – axis and the parabola y² –…

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Q: Find the surface area of revolution about the x-axis of y=3sin(5x)y=3sin(5x) over the interval…

A: I am attaching image so that you understand each and every step.

Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

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Q: Determine the area bounded by the ellipse satisfying:(101x+ 10y)2+ (20x+ 2y)2= 1.

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Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

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Q: Find the area of the region bounded by the curves y= 2² - 3 and y = 2x + 5.

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Q: Find the area of the region bounded by the parabola y = 3x2, the tangent line to the parabola at (3,…

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Q: 7. Find the radius of gyration of a plate covering the region bounded by y3,x 2, and the x-axis with…

A: Formula used:Radius of gyration, moment of inertia and area under curve with reference to y axis is…

Q: Find the area of the region bounded by the parabola y = 4x², the tangent line to this parabola at…

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Q: rea of the region enclosed by

A: we have to find the area of the region bounded by the curve, y=2-x2 .....(1) and the line y=-x

Q: 5. Sketch the region bounded by the two curves y=10x-x* and y=x². Calculate the volume of the solid…

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Q: Find the centroid of the region cut from the first quadrant by the circle x2 + y2 = a2.

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Q: The area of region bounded by the parabola y2 = 4x and the line %3D y = 2x – 4 is

A: We have to find the area of the region bounded by the parabola y2=4x and the line y=2x-4 .

Q: Find the area of the region bounded by the hyperbola 25x² – 4y² = 100 and the line x = 3.

A: We have to find the area of the region bounded by the hyperbola 25x^2-4y^2=100 and x=3  Please see…

Q: 4) Use integration to find the area of the ellipse 4x² + y² = 9.

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Q: find the center of mass of a thin plate of constantdensity d covering the given region The region…

A: Given :                 y = 2x2 - 4x  and y = 2x - x2    Graph :…

Q: Parabola with equation y = x^2, correct and calculate the area of ​​the region bounded by the…

A: Given a parabola y=x2 We've to find the area of the region bounded by the y-axis and tangent to the…

Q: Compute the area contained between the parabolas y and y 3 = 4 --x2

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Q: Q3: Develop the lateral surface of a hexagonal prism of base edge 20mm a on its base on HP such that…

A: Given: To explain the given statement as follows, To develop the lateral surface of a hexagonal…

Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y – axis and the parabola y2 –…

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Q: What is the area of the region bounded by the parabola y^2 = 2x and the line x-y-4 = 0? *

A: See the details solution in below

Q: 4) Calculate the area of the domain bounded by the parabola y = x², the hyperbola y = and the line y…

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Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A: The equation of the parabola is given by y = 4x2.Differentiate y = 4x2 with respect to x as follows.

Q: For the pink region bounded by a parabola with vertex at (-1, 11 ) and the green line, solve for: a.…

A: The given equation of the parabola is y=-a(x-h)2+k, with vertex -1,11. ⇒y=-a(x+1)2+11 Given two…

Q: 2) Find the area of the region bounded by two parabolas x = y2 - 5y, and x=3y - y? . Specify the…

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Q: Find the area of the region bounded by the parabola y = x2, the tangent line to the parabola at the…

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Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

A: The given parabola is: y=2x2 The tangent line at (5,50) has the slope: mx=5=dydxx=5          =4xx=5…

Q: h -y =

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Q: Find the area of the region bounded by the curves, y = -6, y = 6,the y – axis and the parabola y² –…

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Q: Find the Area of a Surface of Revolution. y=1/3(x3), [0,3]

A: Given, y=13x3   interval :0,3

Q: Calculate the area of ​​the region enclosed by the parabolas  y=x2 and y=2x−x2.

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Q: Find the area of the region enclosed by parabola y=3-x2 and the line  Y=3-2x

A: We have to find the area of the region enclosed by parabola y=3-x2 and the line y=3-2x. The point of…

Q: Find the area of the region bounded by the parabola y = -x² + 4x - 3 and | its tangent lines at the…

A: We have to find the area of the region.

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)^2=2y , the…

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Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

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Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

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Q: 12. Informally explain how a surface area generated by a curve of rotation can be computed with an…

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Q: The arc y=2 sqrt(x) from x∈[4,16] is rotated about the x axis. Find the exact surface area…

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Q: Find the area of the region enclosed by the line y = 2x + 4 and the parabola y = 4 - x2 in the…

A: The diagrammatic representation of the area is,

Q: Find the center of mass of a thin plate of constant density δ covering the given regions. The…

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Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y – axis and the parabola y2 -…

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Q: 4. Figure 4 shows the region R in the first quadrant bounded by two curves y =(4- x²) and y =(4- x²)…

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Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y – axis and the parabola y² –…

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Q: Find the area of the region bounded by the curves, y = -6, y = 6 , the y – axis and the parabola y2…

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Q: Find the area of the surface generated by revolving the region bounded by, 1 + 6 y 1<x < 3 16x4…

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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.