Find the volume of the solid generated by revolving the curve y=3vx between x = 0 & x = 3 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: Find the volume of the solid formed by rotating the region bounded by the curve y = v3 and the line…

A: Follow the procedure given below.

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: 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 generated by revolving the curve y? – x8 – x2 = 60 between x = 0 - and…

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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 generated by revolving the regionbounded by the parabola y = x2 and the…

A: To find volume of solid

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 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 by revolving the “triangular” region bounded by the x-axis,…

A: Given information:

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: 3. Find the volume of the solid generated by revolving the curve y = 5Vx between x = 0 and x = 4…

A: We can solve it by cylindrical method.

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

A: Given: y=x3, y=1, x=0 &amp; x=1 From the given curve the bounded region is as shown below: Apply…

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

A: The equation of the line is y=2 and the equation of the curve is y = sec(x)tan(x)  The intersection…

Q: Find the volume of the solid generated by revolving the region between the curves y = x² and y = vx…

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Q: Find the volume generated by revolving the area enclosed by the curve x^2+y^2=16 about the y-axis.

A: here volume is ∫πy2dx here the limit is if we put y=0 in equation so x range from -4 to 4 so   V=…

Q: Find the volume generated by revolving the curve y = cos(2x) about the x-axis, 0 < < 4

A: Given:       y=cos(2x) , 0≤x≤π4

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: Find the volume of the solid generated by revolving the region bounded by the line y = 0 and curve y…

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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 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: 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 revolving the curve defined by 9x²+4y²=36 about the line…

A: Given, The volume for solid revolution between the curves and around the on interval [0,1] The…

Q: Find the volume of the solid generated by revolving 67 from y = 1 to y= 2 about the y-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: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 16 about the y-axis

A: Given Data: Curve: x2+y2=16   The figure below indicates the graph of the curve.   The intersection…

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 the curve x = e^y2 y = 1…

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Q: Find the volume generated by revolving one arch of the curve y = sin x about the x-axis.

A: Let the bounds of one arch of the sine curve be 0 and pi. Then, the volume generated by revolving…

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

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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 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 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 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 generated by revolving about the y axis the region under the curve…

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Q: Find the volume generated by revolving the area enclosed by the curve x² + y = 25 about the y-axis.

A: We have the curve x2+y2=25 rotated about y-axis.

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

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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 of the solid formed by revolving the area bounded by y = sin(x^2), x epsilon…

A: Given that y=sinx2 , 0,π find the volume of the solid obtained by rotating around y axis…

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,…

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

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.