Calculate the volume enclosed by the surface that is created when one rotates the curve y = a² b4 about the x-axis, assuming that 0

Q: Determines the volume generated by curves x² + y² =25 and y² - 6x +15= 0, when rotating around the Y…

A: Given: x2+y2=25 y2-6x+15=0 To find: Volume generated by the given curves when revolved about…

Q: - Find the volume of the solid generated by revolving the region Enclosed by the curve (y-√√4x²,…

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Q: 4. Find the volume generated by revolving the area cut off from the parabola y = 4x - x² by the x…

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Q: Find the volume of the solid generated by the area bounded by the curve y = x³,x = 1,x = 2 and y = x…

A: The volume of a region is the integration of the area of the region. It can be calculated using…

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

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Q: Find the surface area of volume generated when the curve y=.5(x^2+1) from x=0 to x=1 revolves around…

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

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Q: Find the volume generated by the area bounded by the parabola x = Vay , and the line y = b that is…

A: As per our guidelines, we are suppose to answer only one question. kindly repost the question as the…

Q: The volume generated when ℝ is rotated about the x-axis.

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Q: Find the volume of the solid generated when the area bounded by the curve y = Vx, the y-axis, and…

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Q: . THe area enclased by the loop of the curved y= x (x - 3)° is Find the volume generated . revolved…

A: Here 1st we will find points where loop is formed and then shade the region bounded ,  To form the…

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 & x=1 From the given curve the bounded region is as shown below: Apply…

Q: Find the volume swept out by revolving the region bounded by the y-axis and the graph of x = t (1 -…

A: Given,

Q: Find the volume generated if the area bounded by the curve x2 = y - 2 is revolved about the x –…

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Q: Find the volume generated if the area bounded by the curve x² = y – 2 is revolved about the x-axis.

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Q: Compute the volume generated by the curve = 4 y = z about x-axis between x = 2 and x x2

A: Given curve is  revolved around x-axis ,so now we will find volume generated by intigration between…

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 of the solid generated by the curve f(x)=4-cosx revolved 360° about the x- axis in…

A: We calculate the required volume using integration. ∫4-cos x2dx=∫16-8 cos x + cos2 xdx=∫16-8 cos x…

Q: Find the volume generated by revolving the area under the curve y=e^x from x=0 to x=1 about the…

A: Volume of the solid obtained by revolving x=g(y) about x-axis is given by,                   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: Find the surface area of the volume generated when of y = x3, on the interval [0, 1], is revolved…

A: We have to find the surface area of the volume generated by the curve by rotating about the y axis.

Q: Find the surface area of the volume generated by the curve y = x^3/3 from x = 1 to x = 2 revolved…

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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: 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 when the area bounded by the curve y = vx, the y-axis, and…

A: Volume is the measure of the amount of space occupied by a closed surface. It is measured in terms…

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: 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: .Find the volume of the solid generated by revolving the shaded region about the given axis. x+ 2y 2…

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

A: In the question we have to find volume of the region bounded.

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: Use the trapezoidal rule with 4 subintervals to find an approximation to the volume of the solid…

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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 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 surface area of the volume generated when the following curves revolve around the given…

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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 if the area bounded by the curve x? = y – 2 is revolved about the x- axis.

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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: Determine the volume generated by revolving the region in the first quadrant bounded by the curves…

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Q: Find the volume, if an area bounded by an asteroid I = cos t y = sin³ t ve y = -/I+x ,y-axis, and…

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Q: find the volume of the solid that results when the region enclosed by the curves x=y2 and x=y+2 are…

A: Given curves are x=y2 and x=y+2          (1) f(y)=y2 and g(y)=y+2 From (1)…

Q: Find the volume of the Solid of revolution when the curve y= 2+4 is revolve d around the x-axis on…

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Q: Find the volume of the solid of revolution when the curve y = x³ +1 is revolved around the x-axis on…

A: The given curve is y=x3+1 To find the volume of the solid revolution when the curve y=x3+1 is…

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: The volume of the solid generated when the region at the first quadrant bounded by the curve y = x²…

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Q: Find the volume generated by revolving the area enclosed by the curve x-+y3D25 about the line…

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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,…

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.