Find the volume of the solid of revolution generated by revolving the region bounded by the graph  y=x sqrt  √ sin(x)  and the x-axis from x=0 to x= pi/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 volume of the solid generated by revolving the region by bounded 2 y = x + 1 , x = 2 and the y -…

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Q: 3. Find the volume of the solid formed by revolving the region formed by the curve y = secx about…

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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: . Find the volume of the solid generated by revolving the area bounded by the curve y = In x, the…

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Q: Find the volume of the solid of revolution formed by revolving the region bounded by y = f(x) = 2x -…

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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: 8. Find the volume of the solid generated by revolving the region enclosed by y = 2 sinx and y = 0…

A: Use the cylindrical method to determine the volume of the region. Substitute the function and limits…

Q: Consider the region bounded by the graphs of y = sqrt(x tan-1 x) and y = 0 for 0 <=x<= 1. Find…

A: Given,

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 formed by revolving the region bounded by y = sin 2x, x = 0, and x =…

A: We need to find the volume of solid formed by revolving the region bounded by the curve about the…

Q: Find the volume of the solid generated when the region between the graphs of the equations f(x) + x…

A:

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

A: y=sinx  &amp;  y=0  for  0≤x≤π

Q: Find the volume of the solid generated by revolving the region bounded by y = 2/sin x, y=0, and and…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the curves 3π y = sin x +…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the curves…

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

A:

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: 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: Graph the given functions as shown below:

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

A:

Q: Find the volume of the solid obtained by rotating the region bounded by the curve y = sin (7x) and…

A: Volume

Q: Find the volume of the solid obtained when the region above the x-axis, bounded by the x-axis, and…

A:

Q: Find the volume of the solid formed by rotating the region bounded by y=sin2(x) and y=sin3(x) from…

A: Consider the given information. y=sin2(x) and y=sin3(x) And, the limit is  x=0 to x=pi. Put the…

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 of revolution generated by rotating about x= -1, the region bounded by…

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Q: Find the volume of the solid obtained when the region under the curve y = x/4 – x2 from x = 0 to x =…

A: Given data:     The given expression is: y=x(4-x2)1⁄2. The given limits of x is: (a,b)=(0,2). The…

Q: Find the volume of the solid generated when the area of the region above the x-axis, bounded by f…

A: The given region is bounded by:  f(x)=12αx      and    x=2

Q: Find the volume of the solid that results when the region enclosed by the curves y = cos x and y =…

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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 generated byrevolving the region in the first quadrant bounded by the…

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Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = tan-1x, x =…

A: The region is shown below:The intersection point of the curve tan-1 x with the line y=pi/4, will be…

Q: Find the volume of the solid generated by revolving the region bounded by by y = cos 2 y = sin =. x…

A:

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

A: 1st we will draw the region bounded and then rotate it about y=-4 to generate solid , To find voulme…

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = sin x + sec…

A: y=sinx+secx,  y=0,  x=0  &amp;  x=π3

Q: Find the volume of the solid obtained by rotating the region bounded by the curve  y=sin(10x^2)…

A: The volume made by full revolution of area under y=f(x) about y axis between limits x=a and x=b is…

Q: Find the volume of the solid generated when the area of the region above the x-axis, bounded by f…

A: Here we have to find the volume of the solid generated when the area of the region above the x-axis,…

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 REGION BOUNDED BY y = 205x - 1 AND THE X-AXIS IN THE INTERVAL πT 317 EX2 IS REVOLVED ABOUT 2 2…

A: The Shell formula for Revolution about a vertical line is used to evaluate the volume of the solid…

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 area of the surface obtained by rotating y = cosh x over [−ln 2, ln 2] around the x-axis.

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Q: Find the center of the mass of a thin plate of constant density 6 covering the region bounded by the…

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Q: Find the volume swept out by revolving the region bounded by the x-axis and one arch of the cycloid…

A: Given:

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 area of the region bounded by the curves y = sin (7x), y + 1 = x², 3x = -2y on the interval…

A: 1st we will draw the solid of rotation and then use cylindrical/shell method to find volume of the…

Q: The volume of the solid obtained by revolving the region bounded by the curve y = x - x² and the…

A:

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.