The curve y = (64x – 4x³ )m bounds the shaded section on top and the x-axis on the bottom. Determine the area of the shaded section and the coordinates of its centroid.

Q: Find the area and centroid bounded by the x-axis and the curve y=2x-x^2. Graph

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Q: Find the area and centroid bounded by the curve 5y? = 16x and the curve y2 = 8x – 24.

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

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

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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: Find the area and centroid bounded by y^2 =12-3x and y=3x. Graph

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Q: Find the centroid of the region with the curves y=x^3 and y=4x in the first quadrant

A: Refer to the figure shown below:

Q: Find the centroid (, y) of the region bounded by: y = 6x2 +9x, y 0, a = 0, and x = 1.

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Q: Find the centroid of the region bounded by y = 9 – x² and the x-axis.

A: Given, y=9-x2or let fx=9-x2and x-axis y=0or let gx=0

Q: Find the centroid of the region bounded by the curves. y=1-x2, y=0

A: We Use the Given Curves Find the Centroid. Firstly We Find Required Area and After we find X and Y…

Q: Find the centroid of the region in the first quadrant bounded by the given curves. y = x7,    x =…

A: Given, y = x7,    x = y7

Q: Find the ordinate of the centroid of the region bounded by the parabola y = -x2 and the line x = 2y…

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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: Q2) Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y = 2x…

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Q: The area of the surface obtained by rotating the curve y = x2, 0sxs1 about the y-axis is

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Q: Find the centroid of the region cut from the first quadrant by the curve y = 1/sqrt(x + 1) and the…

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Q: Find the centroid of the region bounded by the curve y=x³ and y=4x in the first quadrant.

A: Formula to find the centroid helps to find the required centroid bounded by the given curves.…

Q: Determine the centroid formed by revolving about the y-axis, the a bounded by the curve y = x*, the…

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Q: Q4/ Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.

A: Topic:- geometry

Q: Find the area of the surface generated by revolving the curve y /2x-x, 0.25 sxs1.5, about the…

A: Use surface area formula about x asis

Q: Find the centroid of the region bounded by the given curves. у %3D 2х — 1, y = x² – 1 -

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Q: Find, to two decimal places, the x-coordinate of the centroid of the region in the first quadrant…

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Q: find the ordinate of the centroid of the region bounded by the parabola y = x^2 and the line y = 2x…

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Q: Determine the centroid of the first-quadrant region bounded by the parabola y = 4 – x²

A: Given; parabola y=4-x^2

Q: Find the centroid of the region in the first quadrant that is bounded above by the lines y = 2x and…

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Q: Find the area and centroid bounded by the curve x=3y-y^2 and the line x+y=3. Graph

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Q: Find the centroid of the region in the first quadrant bounded by the given curves. y = x*, x = yA

A: Given curves, y=x4x=y4 The formula for the centroid of the region bounded by the curves f(x) and…

Q: Most centroid calculations for curves are done with a calculator or computer that has an integral…

A: Given: The coordinate of the centroid of the curve

Q: Find the area of the surface obtained by rotating the curve y = √(5-x),   3≤x≤5 about the x-axis.

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Q: Find the centroid of the region bounded by the x-axis, the curve y = sec x, and the lines x =…

A: Consider the graph. The graph is symmetric across x = 0.

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: The area of the surface obtained by rotating the curve y = 17 x +1, 0SXS 34 about the x-axis is

A: The solution are next step...

Q: Find the area of the surface generated by revolving the curve y=x3/3 from x=0 to x=1 about the…

A: To find the area of surface generated by y=x33 and x=0,x=1 about x-axis A=∫012π·y·dS, dS=1+y'2·dx,…

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

A: The region bounded by the curves 2x2+4x+y=0 & y=2x is as shown below.

Q: Find the area of the surface generated by revolving the curve y = - V6 sxs0, about the x-axis. 24'

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Q: Find the area of the surface obtained by rotating the curve y = 2x 223 from x = 0 to x 2 about the…

A: HERE THE LIMITS OF INTEGRATION IS 0 to 2.

Q: Find the area of the surface obtained by rotating the curve y=1+3x² from 0 to x = 9 about the…

A: Let's find area of surface obtained by given curve.

Q: Find the centroid of the region bounded by the graphs y=6– x² and у %33 — 2х.

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Q: Find the centroid of the region that is enclosed between: y = 0 and y = 1- x².|

A: To find the centroid of the region that is enclosed between: y=0 and y=1-x2.

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

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Q: Find the area of the surface generated by revolving the curve y =2x-x, 0.5sxs1, about the x-axis.

A: To calculate the area of the surface we use the formula A=2π∫abf(x)1+((f'(x))2 dx

Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

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Q: Find the centroid of the region bounded by the parabola y=x2 and the line y=4.

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Q: Find the area of the surface obtained by rotating the curve y =÷x/2 – x³/2 for 0 < x < around the…

A: We find dy/dx using power rule

Q: Find the centroid of the region bounded by the graphs y = x2 and y = 5x + 14. NOTE: Enter the exact…

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Q: The area of the surface obtained by rotating the curve y = V9-x2, -3 < x < 3 about the x-axis is

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Q: Find the centroid of the semicircular area inside x2+ y2 = a2 with y ≥ 0. Show the graph for it.

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Q: x = 1+ 2y2, 1< x < 2 about the x-axis.

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Q: 2

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Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: Locate the centroid of the shaded area between the two curves.

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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.