The area bounded by y = 3, X = 2, y = -3 s and x = 0 is revolved about the y-axis 10. The x-coordinate of its centroid is. А. О В. 1 С. 2 D. 3

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: Where is the centroid of the region bounded by y = 4-x2 and the x-axis?

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Q: Find the area of the reglon bounded by the graphs of the equations. y = -x+ Bx, y = 0

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Q: B) Find the area of plate bounded by y =x-1,y =3-x and y 0.

A: The area is the measure of the amount of space occupied by a plane figure. It can be expressed in…

Q: compute the surface area of revolution about the x-axis over the interval. y= x3, [0, 2]

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Q: Find the moment about the r-axis of the lamina bounded by the upper half of (x – 1)2 + y² = 1 and…

A: Given lamina:  x-12 + y2=1 The positive part of the given lamina,  y=fx = 1-x-12…

Q: find the Area between x=y^2-2, x=e^y. Y=1, y=-1.

A: Given The region, x=y2-2, x=ey and y=1, y=-1 To find the area of the given region.

Q: What is the volume of the solid whose 1 30 cross-sections are squares perpendicular to the x-axis…

A: Given: The region bounded by the curves are: y=x and y=x The cross-sections are squares…

Q: Find the area of the unbounded shaded region. y = ex/5 у 2.0 1.5 1.0

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Q: The area bounded by y^2 + x - y = 1, y-axis, and the line 2y = 9 is revolved about the line x = 1…

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Q: The area bounded by the curve y^2 = 4x and the line 2x -y = 12 is revolved about the y-axis. Find…

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Q: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

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Q: Find the centroid of the area bounded by the curves y = x^3, x = 0 and y = 8

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Q: 2. The area bounded by y = -(x – 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about the…

A: Given: The area bounded by the curves which are: y=-12(x-1)2+4 and the lines x=1, y=2 and y=4 And…

Q: Q2/ The region bounded by the curve y = x² and the line y = 3x, in the first quadrant is revolved…

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Q: 1. Find the area bounded by the curves y – 2 = x² ,y = 6 and the y – axis ( in Quadrant I only), as…

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Q: The area bounded by the curve y = VT, the y-axis and the line y = 2 is revolved about the line y =…

A: The given curves arey=x, and the y axis and the line y=2 is revolved about the line y=2now since…

Q: Compute surface area about the x-axis over the interval y= 4-x23 2,[0,8] 2/3 3/2

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Q: Find the centroid of the area under y = 4 – x^2 in the first quadrant.

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Q: Compute the surface area of revolution about the x-axis over the interval [3, 5] for y = 2x + 4.

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Q: 2. Find the surface area when y = 2\x with 1 < x < 3 is rotated around the x axis.

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Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

A: Solution is given below:

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 4x³. (Use…

A: In this question we have to find the surface area of the revolution about the x-axis.

Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

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Q: compute the surface area of revolution about the x-axis over the interval

A: The given function is

Q: How far is the centroid of the area bounded by the curves y = e^x, y = e^-x, and x = 1 measured from…

A: Centroid

Q: Determine the position of the y-centroid of the area between the curve y = 7.2/x and the x-axis from…

A: Suppose the region bounded by two curves f and g on   then centroid or center of mass of the region…

Q: Compute for the volume of the solid formed bounded by the equations (y- 4)2 = x - 3, x-10, y-4, and…

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Q: Compute for the area of the figure bounded by the curve y = x³, y = 8 and x = 0.

A: Given : y = x3 , y = 8 and x = 0. To find : Area of figure bounded by the given curve and lines?

Q: 5. Find the area of the surface of revolution generated by revolving .3 y = on interval [0,3] about…

A: Given: The function y=x33on interval 0,3, To find: The area of the surface of revolution generated…

Q: The area bounded by the curve y^2 = 4x and the line 2x - y = 12 is revolved about the y-axis. Find…

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Q: Find the area M and the centroid (š, §) inside curves 12 y = x. ' = 2-x, j' = {) (triangle)

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Q: Determine the centroid of the area bounded by y? = 2x and the line x - y = 0.

A: Given curves are y2=2x ,x-y=0 we have to find the centroid of the area bounded between the curves.

Q: How far is the centroid of the area boundded by the curves y=e^x, y=e^-x, and x=1 measured from the…

A: We have to find the distance of centre of mass from y Axis  So , find only x coordinate of centre of…

Q: 23) Find the area of plate bounded by y = x- 1, y = 3-x and y = 0.

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Q: The region bounded by the curves y = x² – 2x and y = 4x is revolved about the line y = -1. Which…

A: The given curve is y=x2-2x and y=4x. Now, find the intersection point of these two curves.…

Q: Determine the ordinate of the centroid of the area bounded by the curve x^2 =8y and the line 2x-y=0

A: Given curves are x2=8y and 2x−y=0. We have to find the ordinate of the centroid of the area bounded…

Q: Find volume y=3x^2, x=1, and y=0 about x axis

A: y=3x^2, x=1, and y=0 about x axis

Q: 2. The area bound by the curve y = ezr, the y – axis and the line y = 4 is rotated about the line y…

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Q: Compute the surface area of revolution of f (x) (x + 1)z about the x-axis over 3 [0,1]

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Q: How far from the x-axis is the centroid of the area bounded by the curve y = 8x, the y-axis and the…

A: Solution is given below:

Q: The area bounded by the curve y 2 - 4x and the line 2x -y 12 is revolved about the y-axis. Find the…

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Q: Q3. The region bounded by the curve y x² and the line y 3x, is revolved about the line x = -3. Find…

A: Here i use cylindrical shell method to find out volume of rotation

Q: The area bound by the curve y^2 = 12x and the line x = 3 is revolved about the line x = 3. What is…

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Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

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Q: Compute the surface area of revolution about the x-axis over the interval [0,1) for y = 4x'. (Use…

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Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2, x = 5 and x-axis.

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Q: compute the surface area of revolution about the x-axis over the interval. y = (4 − x2/3)3/2, [0, 8]

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Q: Find the centroid of the area in the first quadrant under the curve y = 4 − x 2.

A: We have to find the centroid of the area in the first quadrant under the curve y=4-x2.

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.