Find the volume of the solid formed by revolving the curve defined by 9x²+4y²=36 about the line x+y=6.

Q: . Find the center of mass of a thin plate covering the region bounded below by the parabola y = x…

A: The given curve is, y=x2 and the line y=x with density δx=12x. Sketch the bounded region as below:

Q: Find the center of mass of a thin plate of variable density  d(x) = 4x2 covering the region bounded…

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Q: Find the volume of the solid obtained by revolving the curve x²=y-3 about x-axis from x=1 to x=3

A: The volume generated by revolving any curve y=f(x) about x-axis  from x=x1 to x=x2 is given by V=…

Q: Find the volume of the solid generated by revolving the region between the parabola x = y² +1 and…

A: Given Data: Curve 1: x=y2+1 ......(1) Curve 2: x=5 ......(2) The graph of the region enclosed by the…

Q: What is the volume of the solid that results when the region enclosed by the curves y = cosx and y =…

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Q: - Find the volume of the solid generated by revolving the region Enclosed by the curve (y-√√4x²,…

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Q: Consider the region enclosed by the curves y = 1 +1 and y = 2x+ 1: 6- -5- The volume of the solid…

A: Finding the volume of solid revolution revolving around x=3

Q: Find the volume of the solid generated by revolving by the curve y = v2 – x² and x-axis: حد د واحدا…

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Q: Find the center of mass of a thin plate of density δ = 3 bounded by the lines x = 0, y = x, and the…

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Q: Find the volume of the solid generated by revolving the region between the curve y = 10 – x² and the…

A: The region is bounded by y=10-x2 and y=1. By Cylindrical shell method, ∫ab2πyfydy Obtain the…

Q: Find the volume of the solid obtained by rotating the curve y=x^2 , y= square root x , the lines x=0…

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Q: Q4) Fid the volume of the solid generated by revolving the region between the curve y = x + 1 and…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: • This is a problem based on the applications of definite integral.  First we have to identify the…

Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x2 and…

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Q: Find the volume of the Solid generated by revolving the region bounded by y = 1/, and the lines x =…

A: According to the given information it is required to find the volume of the solid generated by…

Q: Find the volume of the solid formed by revolving the area bounded by the parabola y2 = 9x and the…

A: We want to find the area bounded by the parabola y2 = 9x and the line y = 3x about the y-axis.

Q: 1- 0.5- x-2 tan 4 2.

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Q: Find the volume of the solid generated by revolving the region between the parabola x=y^2+1 and the…

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Q: What is the volume of the solid rotated about the x-axis under the curve y = 2x -1 from x = 1 to x =…

A: Volume by disk method: The volume of a shaded region bounded by two curves over the interval [a,b]…

Q: Find the surface area generated by revolving y=7x+6 about the x axis on the interval [0,6]

A: We need to find the surface area generated by revolving y=7x+6 about the x axis on the interval…

Q: Find the volume of the solid formed by revolving the region bounded by the curves y = 3x²,x = 0, and…

A: Given : Curves y = 3x2, x = 0 and y = 3   To find : Volume of solid formed by revolving the region…

Q: Determine the area of the surface generated by revolving y=x³ on (0,1), about the x-axis.

A: The given curve is y=x3  on 0, 1 about x-axis. This implies that,…

Q: Find the volume of the solid obtained by revolving y = sin x for 0 ≤ x ≤ π about the x-axis.

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Q: Calculate the volume of solid of revolution when the region bounded by y = sin 2x and x² - y2 = 0 is…

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Q: Find the volume of the solid generated byrevolving the region in the first quadrant bounded by the…

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Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the line y…

A: Explained below

Q: Find the volume of the solid formed by revolving the region enclosed by the closed curve 4x2 +9y² =…

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Q: Find the volume of the solid generated by revolving the curve y=3vx between x = 0 & x = 3 about the…

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Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

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Q: Find the volume of the solid generated when the region under the curve y = x2 over the interval [0,…

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Q: Find a center of mass of a thin plate of density 8 = 5 bounded by the lines y = x and x=0 and the…

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Q: Find the volume of the solid generated byrevolving the region in the first quadrant bounded by the…

A: Using Shell Method:             2π∫01x.e-x dx Limits come from where the column can be created. (in…

Q: Find the volume of the solid of revolution generated by revolving y = 9-x from x= - 3 to x= 3 about…

A: Given f(x)= 9-x2    where -3≤x≤3 To find the volume of the solid of revolution here use The Disc…

Q: The volume of the solid generated by revolving the curve y = 2 x, between x =0 and x=3 about the x-…

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Q: Find the volume of a solid obtained by revolving the curve x2=y-3 about x-axis from x=1 to x=3

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Q: Find the volume of the solids generated by revolving the region bounded by the curves y = 7r² and y…

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Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the line y…

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Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x 2…

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Q: THE AREA BETWEEN THE CURVES 2 4y = x² AND Y²³ = 4X 15 REVOLED ABOUT THE LINE X= -1. SOLVE FOR THE…

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Q: Find the volume of the solidgeneruted by revolving the region between the x-axis and the curve…

A: We first find where y=x2-2x and x-axis meets.x-axis means y=0.So, 0=x2-2xor, 0=x(x-2)or, x=0, 2 The…

Q: Find the volume of the solid generated by revolving the bounded region between the parabola x = y²…

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Q: Find the volume of the solid generated by revolving the region bounded by the parabola y = 2x2 and…

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Q: Find the volume of solid formed by revolving region by f(x)=x^(2/3), x=0, y=0, y=1 about the y-axis.

A: Given:

Q: Find the volume of the solid generated by revolving the region in the first quadrant bounded above…

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Q: Find the volume of the solid generated by revolving about the line y = -3 the region bounded by the…

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

Q: Find the volume generated by revolving the area enclosed by the curve 4y² = 4x²-x+ about the y-axis.

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Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

A: By using volume of a solid formula, we calculate the required volume.

Q: Find the volume generated by revolving the area enclosed by the curve 4y² = 4x²-x* about the y-axis.

A: Hint: First obtain the values of x for which y is zero to obtain the limits of the integration. Now,…

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.