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.

Q: Determine the volume of the solid formed when the region enclosed by the curve y = √x, x -axis and…

A: Given regions are y=x, y=0 and x=4.

Q: Find the volume of the solid Formed by revolving the bounded by the graphs oF fox) =v9-X, y-axis %3D…

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Q: Find the volume of the solid generated by revolving the region by graph of function f(x) 10 ;x 1.25,…

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Q: 14-X %3D (0,4) about the line y=4

A: The given equations are y=4-x, y=0,x=0 on the interval 0,4 and is rotated about the line y=4. Sketch…

Q: Find the volume of the solid generated by revolving about the line y=-1 the region bounded by the…

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

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Q: The area bounded by the curve y = x,y% = 2x and y = 4 is revolved about the line x =-2 Determine the…

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

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Q: What is the volume of the solid that is generated by revolving the region bounded by the curve y=…

A: Given curve is, y = 2x - x2 the volume of solid formed by revolving the region bounded by the curve…

Q: Find the volume formed by rotating the region above the curve y=x^3 and under line y= 1 about…

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Q: Find the Volume of the solid obtained by rotating the curve 1 for 1 < x < 4 1+ x2 around the line r…

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Q: Find the volume of the solid generated from revolving the region bounded by: y=x^3 y=0 x=3…

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Q: The volume obtained by rotating the region bounded by y=36-(x-3)2 and the x-axis about the line x=…

A: Given Region bounded by curve  y=36-(x-3)2, x-axis  (means y=0) about line x=10. the maximum y is…

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

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Q: Find the volume generated by revolving the region above the curve y=x3 , under the line y=1, and…

A: Figure of y=x3 , y=1 and x=1

Q: : Find the center of mass of a thin plate of constant density covering the region bonded by y = 25 -…

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Q: find volume of solid 3x^2 ,x=1, y=0 about x axis

A: Consider the region bounded by the curves y=3x2,x=1,y=0 as shown in the figure below: Here, the…

Q: y = 9x² and y = 0 about x = −4

A: Given:        y=9-x2 and y=0         x2=9           x=3 about x=-4

Q: The area bounded by the curve y^2 = 4x and the line 2x - y 12 is revol %3D about the y-axis. Find…

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Q: To find the volume of the solid generated by revolving the area bounded by the given curve about the…

A: The volume of the solid generated by revolving the area bounded by the curves f(x) and g(x) over the…

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

A: Recall: Disk Method: we consider a region bounded by the graph of the function y=f(x) , the x-axis…

Q: Find the volume generated by revolving the area bounded by y = x3 – x2 , x-axis, about y-axis by…

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Q: Find the volume generated by revolving the area bounded by the curve y = (1 − x2)2 and the x-axis…

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Q: Find the center of mass of a thin plate covering the region bounded above by the parabola y = 4 - x2…

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Q: Use differential to calculate the volume of the material needed in making a thin sphere with inner…

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Q: Find the volume generated by revolving about the line x=0 the area bounded by the curve y^(1/2) =…

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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 generated by revolving the region bounded by y =4(sqrt(sin x))​, y = 0,…

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Q: Find the volume of the solids generated by revolving the region bounded by the function y = x³ on…

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Q: Find the volume of the solid generated when the area bounded by the curve y = square root of x,…

A: Find the volume of the solid generated when the area bounded by the curve y=x, y-axis and the line…

Q: Find the volume of the the solid formed by revolving the region bounded by y=5-x; y=0; about the…

A: Integration of function expression with respect to variable x or y gives the area between function…

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

A: Given functions are                                                         y=x2y=3xx=-3 points of…

Q: Find the volume of the the solid formed by revolving the region bounded by y=5-x; y=0; about x-axis.…

A: Double integrating the region or integrating the area of a region gives the volume. Use proper…

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 generated by revolving the shaded region about the x-axis: y = sinx…

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Q: Find the volume of the solid obtained by revolving the region bounded by the curve y=1 / (1−sinx)…

A: We have given a region bounded by the curve y=11-sinx, 0≤x≤π3the region is show in the graph-

Q: The area bounded by the line x=1 and the curve y^2-x=3 is revolved about the line y=4. Using Shell…

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

A: Topic = volume

Q: Find the volume of the solid whose base is the region enclosed between the curve x = 1−y² and the…

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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 generated by revolving the area bounded by the given curves about the…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: The region bounded by the curve (y = x2 + 5) and the line (y = x+7) is revolved about x-axis to…

A: The intersection points of the given curve and the line is calculated as follows:…

Q: Find the volume (in cubic units) of the region bounded by the curves y' = 4x and the line X = y when…

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)=8x$ on 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 of revolution generated by revolving the region bounded by the graphs…

A: Solution is given below

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

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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.