Find the volume of the solid generated by revolving the curve y² – x1l – x² = 64 between x == 0 and x = 2 about the x – axis.

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: the area between the curves 4y=x2 and y2=4x is revolve about the line x= "-1." solve for the volume…

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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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 volume of the solid of revolution obtained by revolving the region under the curve y = f(x)…

A: Use formula of volume revolved about x axis

Q: Find the volume of the solid generated by revolving the curve y? – x8 – x2 = 60 between x = 0 - and…

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

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Q: nd the volume of the solid generated by revolving the area bounded by y = x2 a axis from [0, 2]…

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Q: What is the solid of revolution obtained when you revolve the region bounded by the curves y=x−1,…

A: We have given curves y=x-1,  y=0 and x=3 And we can plot graph of these curves as We can  see here…

Q: Find the volume of the solid of revolution obtained by revolving the region under the curve y = f(x)…

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

Q: Q1/ Find the volume of the solid generated by revolving the region bounded by the line (y= x+3 ),…

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Q: Find the volume of the solid generated by revolving the curve y = vx,between x = 0 and x 4 about the…

A: In such type of questions curve given in terms of x i.e. y=f(x) and rotated about x axis. Then…

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 of revolution generated by revolving the region bounded by the graph…

A: Here,  we need to find the volume of the solid of revolution generated by revolving the region…

Q: Find the surface area for the solid of revolutic -1< x<1 about the x-axis.

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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: Compute the volume of the solid obtained by revolving the curve y = vx sin x about the x-axis…

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Q: The volume of the solid generated by revolving the region bounded by the curve y = cos 2x, 0Sxs4…

A: (π^2)/8  cubic units

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 obtained by revolving y = sin x for 0 ≤ x ≤ π about the x-axis.

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Q: Find the volume of the solid formed by y = 4 sin(x) bounded by x = 0 revolved about the x axis on…

A: We have to find the volume of the solid formed by y=4sinx bounded by x=0 revolved about the x axis…

Q: 2. Find the volume of the solid generated when the region between y = sin x and y = 0 for 0 ≤ x ≤ π…

A: The region between y=sin x and y=0 for 0≤x≤π is revolved about the y-axis.

Q: y = -0.0159x* + 0.2301x3 1.2034x2 + 2.6595x + 0.0661 What is the volume of this solid of revolution…

A: We know that Volume of solid formed by revolving the region bounded by the curve y=f(x) and the…

Q: Q4. Find the volume of the solid generated by revolving the curve r- between y=1 & y=4 about the…

A: We have been given the function which varies between y = 1 and y = 4 and revolves around y-axis.…

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: What is the volume of the solid formed when rotating the region bounded by f (x) =-x² + 7x – 12 and…

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Q: The volume of the solid generated by the curve y = e¯*, between x = 3 and x = 8 about the axis is -…

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Q: Find the surface area generated by revolving y=5x+2 about the x axis on the interval [0,6]

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 7x^5 on the…

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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 solid of revolution generated by rotating the curve y = x³ O and y = 4 about…

A: Here, to use the above formula the function is of the form f(y), so here y=x3⇒x=y13

Q: Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

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Q: The volume of the solid generated by revolving the curve x = 4, about the y-axis between y= 0 and y…

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Q: The area under the curve 4y2 =" (x2 + 1)3 was rotated about a line located to the left of y – axis…

A: The surface area of the solid can be obtained using the Pappus theorem. The surface area is…

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: The volume for solid of revolution between the curves y = v(49- x^2) and y = 0 around the x - axis…

A: Let's find volume of solid of given curves.

Q: Find the volume x=y-y2; x=0 revolving at y-axis

A: Given problem:- Find the volume x=y-y2 ; x=0 revolving at y-axis

Q: Find the volume of the solid of revolution generated by revolving y = (e^−x) + 2around the x-axis…

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Q: Find the volume of the solid of revolution when the curve y = x³ +1 is revolved around the x-axis on…

A: The given curve is y=x3+1 To find the volume of the solid revolution when the curve y=x3+1 is…

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: a) Volume of a solid obtained by revolving about the y-axis Hhe region boonded abon O4 y T on the…

A: Concept introduction: Shell method The volume for solid of revolution between curves is the volume…

Q: Find the volume of the solid generated by revolving the regionbounded by y = √x and the lines y = 2…

A: To find the volume of the solid generated by revolving the region bounded by  y=x and the lines y=2…

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.