Find the volume of the solid obtained by rotating the region bounded by y=sin(5x^2),  y=0,  0≤x≤sqrt(pi/5) about the y-axis.

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: Find the volume of the solid obtained by rotating the region bounded by y= 54x-6x2 and y= 0 about…

A: Given:           y=54x−6x2 and y=0  about y−axis.

Q: Find the volume of the solid generated by revolving the region bounded by y=x+3, y=4 and x=5 about…

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the…

Q: FIND THE VOLUME OF THE SOLID GENERATED WHEN THE REGION BOUNDED BY THE CURVE (x-5)² = 4-Y AND THE…

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Q: Find the volume of the solid formed by revolving the region bounded by f (x) = 4x – x² and the…

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Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y-2= 0 is…

A: We know that if y=f(x) ,and y=g(x) are two curve intersecting at  x=a and x=b  the required volume…

Q: Find the volume of the solid generated by revolving the region bounded by the |2x| about the x-axis.…

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Q: Find the volume of the solid generated by revolving the region between y = 4 – x2 and y = -x + 2…

A: The given regions are, y=4-x2 and y=-x+2 and the given line is, x=44-x=0 We can write the given…

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 of the solid of revolution formed by rotating the area under y=9-x2 over [0, 3]…

A: Given curve is y=9-x2 ,[0,3]

Q: Find the volume of the solid whose base is the region bounded between the curve y = x2 and the…

A: Given that the solid whose base is the region bounded between the curve y = x^2 and the x-axis from…

Q: Determine the volume of the solid formed by revolving the area bounded by y= x- 2x and y=0 about the…

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x)and the x−axis…

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

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Q: Find the volume of the solid generated obtained by revolving the region bounded by y = vx +1 x=3 x=1…

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Q: Find the volume of the solid generated from revovling the area of the region bounded by the curve y…

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Q: Find the volume of the region bounded by: y= 0 X =0 x - V3 that is rotated about the x-axis

A: Here is the solution of the given problem. DISK METHOD:

Q: Find the volume of the solid whose base is the region bounded between the curve y = x³ and the…

A: As per the company policy i can answer only first question for you, More than one answer lead me…

Q: Find the volume of the solid generated by revolving the region bounded by x= square root (1-y^2) and…

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Q: Find the volume of the solid generated by revolving the region bounded by the y = x2 and y=6x-2x2…

A: Given that y = x2 and y = 6x- 2x2 and we find volume about the y-axis and plot the graph. Here i…

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^2=x, x-axis and the line…

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

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Q: Determine the volume of the solid obtained by rotating the region bounded by y = 2vx – 1 and y =x-1…

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Q: Find the volume of the solid obtained by revolving about the line x = 4 the region bounded by y = x…

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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 region bounded by x = (1- y). x= 2,/y and…

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Q: Find the volume OF the solid Formed by revolving the region bounded by the graphr of x- -y't 4y, and…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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Q: Find the volume of the Solid generated by revolving the region bounded by y = -2x² and y = x² – 3 ,…

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Q: Find the volume generated by the region bounded by the curve 4x = y² and the line x - 4 = 0, rotated…

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Q: Calculate the volume of the solid obtained by rotating the region bounded by the curve y=2x-x² and…

A: Sketch the region and integrate in x variable.

Q: What is the volume of the solid obtained by revolving about the x-axis the region bounded by y - 2x2…

A: The general formula for the volume of solid is v=∫abπ(upper curve2-lower…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y=2x2+1 and…

A: First draw the both curve and find the region which will be rotated about x-axis.than use disc…

Q: find the volume “V” obtained by revolutionizing the region between y=x2  and y=12-x around the axis…

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Q: What is the volume of the rotator formed by the function y = 2-x ^ (2) and rotating the region…

A: Let us consider the curve y=f(x) The volume of the solid of revolution about x-axis is obtained by…

Q: Consider the region bounded by y=x² and y=x in the first quadrant. What is the volume of the solid…

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Q: Find the volume of the solid generated by revolving the region between the y-axis and the curve x =…

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Q: Find the volume of the solid formed by rotating the region between the y=sqrt(x)curve  y=2 line and…

A: The volume of the solid of the revolution can be calculated using integration. The formula for the…

Q: Find the volume of the solid generated by revolving the region bounded by y = x2 - 2x + 2, x = 0, x…

A: Given: The region is bounded by the curves : y=x2-2x+2, x=0, x=1 and y=1 We have to find the volume…

Q: Find the volume of solid formed when the region bounded by y = x² and y = Vx are revolved about…

A: To find the volume of solid formed when the region bounded by y=x2 and are revolved about x-axis…

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

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Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y - 2 = 0…

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Q: Find the volume of the solid obtained by rotating the region bounded by y-2vx-1 and y=x-1 about the…

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Q: find the volume of the solid formed by revolving the region bounded by y = sinx and the x-axis from…

A: From the volume of solid formed by rotating the given function y

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.