Find the centroid of the region bounded by the graphs of the functions y=2sin(x),y=1/7x,andx=π/2y, and touching the origin. The centroid is at (¯x,¯y) where ¯x =    ¯y =

Q: Find the centroid of the region bounded by the given curves. y = 8 sin(4x), y = 8 cos(4x), x = 0, TT…

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Q: Find the centroid of the solid bounded by x² = 4y and y = 5x - x² about the x-axis.

A: We will draw the region and rotate it about x-axis to create a solid of revolution . We will need…

Q: Consider the region bounded by the graphs of y = ln x, y = 0,and x = e. Find the centroid of the…

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Q: find the centroid of the region lying between the graphs of the functions over the given interval. y…

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Q: Find the centroid (¯x,¯y)(x¯,y¯) of the region bounded by: y=3x^2+7x,   y=0,   x=0, and   x=6

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Q: Find the centroid of the region in the first quadrant bounded by the given curves. y = x°, x = y9…

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Q: The region bounded by y = v9– x² and y = 0 has an area of . Find the y-coordinate of its centroid.

A: Suppose the region is bounded by fx and gx on a,b where fx≥gx .Assume centroid is denoted by x¯,y¯…

Q: Find the centroid of the region above the X axis that is bounded by the Y axis and the line Y = 3 -…

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Q: Find the centroid (¯x,¯y) of the region bounded by: y=8x2+9x,   y=0,   x=0,   and    y=0,   x=0,…

A: Given data: The first function given is f(x)=8x2+9x. The second function given is g(x)=0. The given…

Q: Find the centroid of the region bounded by y = 9 − x^2 and y = 0

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Q: Find the centroid of the region bounded by y=x^2 and y=2.

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Q: Find the centroid of the region bounded by the given curves. y = 6 sin(3x), y = 6 cos(3x), x= 0, x =…

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Q: Find the centroid of the region bounded by the given curves. y = 6 sin 5x, y = 6 cos 5x, x = 0, x =…

A: According to the given information it is required to calculate the centroid of the region bounded by…

Q: Find the centroid of the region that is bounded by the line Y = 3X, the line X 2 and the X axis.

A: To find the centroid

Q: Find the centroid of the region bounded by the given curve. y= sin(2x), y = sin(x), OSxs

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Q: Find the exact coordinates of the centroid for the region bounded by the curves y = 4 – x² and y =…

A: The coordinates of the centroid of the area bounded under the curve of the function y=f(x) in the…

Q: Find the centroid of the region bounded by the graphs of y = x + cos x and y = 0 for 0<=x<=…

A: Graph is given below:

Q: Find the centroid of the region bounded by the graphs of the functions y = 7x², y = x² + 7 The…

A: Since,  y=7x2 & y=x2+7 7x2=x2+7x=76,-76

Q: Find the centroid of the homogeneous lamina bounded by the graph whose borders are f(x) = 16 − x2…

A: Let k be the density of the lamina body which is bounded by f(x) and (x-axis)

Q: Find the coordinates of the centroid of the region bounded by the curves y= 1 / x, y = 0, x = 1, x =…

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Q: Find the centroid of the region bounded by the graphs of the functions y 7x, y = x + 4 The centroid…

A: Given,           and

Q: Find the exact coordinates of the centroid for the region bounded by the curves y=4−x^2 and y=0.

A: Given, y=4-x2, y=0 Here 4-x2=0⇒x2=4x=±2

Q: Find the area and the x-coordinate of the centroid of the region bounded by y = x² and y = vx in the…

A: The total region between both curves gives the required area. Integration of the given curves under…

Q: Find the centroid (¯x,¯y)(x¯,y¯) of the region bounded by: y=2x^2+2x,   y=0,   x=0,   and   x=4

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Q: Find the centroid of the region bounded by the graphs of the functions y = 5 sin(x), y -x, and x = 5…

A: we need to find the centroid of the following shaded region The upper curve is y=5sin(x),  lower…

Q: Find the centroid of the region bounded by the given curves. y = 6 sin 3x, y = 6 cos 3x, x = 0, x =…

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Q: Find the centroid along the y-axis of the plane area bounded by the equation y^2=4x, x=1 and the…

A: Given curve is y2=4x ,x=1

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: Find the area and centroid bounded by y^2=-x, x^2+3y+4x+6=0. Graph

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Q: Find the centroid of the solid generated by revolving the region about the indicated axis the area…

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Q: Find the centroid of the region bounded by the given curves. y = 8 sin(4x), y = 8 cos(4x), x = 0, TT…

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Q: Find the centroid of the region bounded by the curves: 2y - y and the y-axis |

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Q: Find the centroid of the region in the first quadrant bounded by the given curves. y = x8, x = y8…

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Q: Find the centroid (¯x,¯y)of the region bounded by: y=4x2+7x, y=0,   x=0,   and   x=3 ¯x=    ¯y=

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Q: Find the exact coordinates of the centroid for the region bounded by the curves y=sqrt(x) and y=x.

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Q: Find the centroid of the region bounded by the given curves. y = 6 sin(5x), y = 6 cos(5x), x = 0, X…

A: In the question we have to find centroid of the region.

Q: Find the centroid of the region bounded by the curve f(x)= x3 on [0,2] and the x-axis.

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Q: Find the centroid of the region that is bounded by the line Y = 3X, the line X = 2 and the X axis.

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Q: Find the abscissa(x) of the centroid of the area bounded by the curves:  y=x2 ,  x=4 and the x axis

A: First, find the area bounded by the curve, y=x2 and the line, x=4, using the formula, A=∫abf(x)dx.…

Q: Find the abscissa of the centroid of the region between the parabola y = 6 − x2 and the line y = 1 −…

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Q: Find the centroid of the region bounded by the given curves. y = 6 sin(3x), y = 6 cos(3x), x= 0, X =…

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Q: Find the centroid of the region bounded by the curves y = 4 and y = x2. %3D

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Q: Find the exact coordinates of the centroid for the region bounded by the curves y = 4-2² and y = 0.…

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Q: 2. Find the coordinates of the centroid of the the region bounded by f(x) = x – x² from x = 0 to x =…

A: Question 2Here we have to find the centroid of the region bounded by f(x)=x-x2; x = 0; x = 1.First…

Q: find the centroid of the region lying between the graphs of the functions over the given interval. y…

A: We would like to find the centroid of the region lying between the graphs of the functions over the…

Q: Find the centroid of the solid generated if the region bounded by X^2 + y^2 - 4y = 0 and y= 4-x and…

A: We have to find the centroid of the solid generated if the region bounded by x2+y2−4y=0 and y=4−x…

Q: Find the centroid (¯x,¯y)(x¯,y¯) of the region bounded by: y=3x^2+8x,   y=0,   x=0,   and   x=6…

A: The region is bounded by the curves, y=3x2+8xy=0x=0x=6

Q: Find the centroid of the region bounded by y = 4x-x and y=-x.

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Q: Find the centroid of the region bounded by the given curves. y = 8 sin 2x,    y = 8 cos 2x,    x =…

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Q: Find the coordinates of the centroid of the region bounded by the straight line y = (2/π)x and the…

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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.