(3+In x) Find the volume of the solid when the curve y=- is rotated 360° about the x-axis between x = e and x = e3.

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: Use cylindrical shells to find the volume of the solid generated by rotating the curve y=2ln(x)…

A: to find the volume of the solid generated by rotating the curve y=2lnx1≤x≤e about x axis

Q: Use cylindrical shells to find the volume of the solid generated by rotating the curve y = 5 ln(x)…

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Q: Use cylindrical shells to find the volume of the solid generated by rotating the curve y = 9 1n(x)…

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

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

A: 1st we will draw the region and rotate it about y axis to generate the solid . As we need to use…

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

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Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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Q: Use cylindrical shells to find the volume of the solid generated by rotating the curve y = 9 In(x)…

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Q: Find the volume of the solid generated by revolving the curve y? - x10 – 22 = 41 between a = 0 and x…

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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 formed by revolving the re-gion bounded by the graphs of y = sin x +…

A: The given graph of the functions are

Q: Find the volume (in units3) of the solid generated by revolving the region under the curve y = 4e−2x…

A: I use cylindrical shell method to find volume about y axis

Q: Find the volume of the solid generated by revolving the “triangular” region bounded by the x-axis,…

A: Given information:

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

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Q: The area enclosed between the two curves x² = 2y and y² = 2x is rotated about the x- axis. Determine…

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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: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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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: The area enclosed between y In (x), the x-axis and x = 3 is rotated about the line x= 3. Calculate…

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

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

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Q: Use cylindrical shells to find the volume of the solid generated by rotating the curve y = 3 ln(x)…

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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 obtained by rotating the curve y = sin² x around the r-axis.

A: The volume of the solid formed by rotating the curve y=sin2x around the x -axis is given by…

Q: Evaluate the volume created under the curve y = sin a +3 from x = 0 to a = ™ when the curve is…

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

A: Solution: By using the cylindrical shell method we have to find the volume of solid revolution of…

Q: Q2) Find the volume of the solid generated by revolving the "tri- angular" region bounded by the…

A: Washer method: To find the volume enclosed between two functions, the washer method is applied. We…

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 shaded region about the given axis.

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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: Between the parabola y = -x² + 4x – 3 and the line y = x – 3 Find the volume of the solid formed by…

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Q: Q3\ Find the volume of the solid generated by revolving the region between the y-axis and the curve…

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

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Q: Use cylindrical shells to find the volume of the solid generated by rotating the curve y=6ln(x)…

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Q: Find the volume of the solid generated by revolving the region enclosed by the graphs of y =…

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Q: *Find the volume of the solid generated by revolving the area bounded by the given curve about the…

A: Given: The area bounded by the curve, y2=4x, x2=4y.

Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the y-axis.

A: Consider the given equation of the circle and find function f(x). Plot the function f(x) and find…

Q: Find the volume of the solid generated by revolving the region bounded by the y2-x2= 1, y = 2 about…

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Q: What is the exact volume of a solid that is formed by rotating the region enclosed by the functions…

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Q: Find the volume, V, of the solid formed, when the part of the curve y = 2x, is rotated about the…

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Q: Find the volume of the solid generated by revolving the unbounded region lying between y = −ln x and…

A: Given that: y=-lnx   and   the   y-axis To sketch the region:

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

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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.