Find the surface area for the solid of revolutic -1< x<1 about the x-axis.

Q: Find the surface area generated by revolving the portion of the curve y=x^2+1 between x=1 and x=2…

A: Given that, Curve, y=x2+1   We have to find the Surface Area Generated by revolving the portion of…

Q: Find the surface area of revolution about the y-axis of y = 3 – 3x over the interval 0 < x <1

A: Given

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 area of the surface formed by revolving the graph of f (x) = x2 on the interval [0,√2]…

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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Q: Find the surface area of revolution about the x-axis of y=3sin(5x)y=3sin(5x) over the interval…

A: I am attaching image so that you understand each and every step.

Q: Determine the surface area generated by revolving the curve y=1/3 x³ over the interval (0,2), about…

A: The given curve is y=13x3  on 0, 2. This implies that, dydx=x21+dydx2=1+x41+dydx2=1+x4y1+dydx2=13x3…

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: Find the area of the surface obtained by rotating the curve y=4x3 from x=0 to x=2 about the x-axis.…

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Q: The surface area of the surface generated by revolving y=x^3 , 0<=x<=1 about the x-axis is

A: We have to find the surface area of the region generated by y=x^3, 0&lt;=x&lt;=1 about the x-axis. I…

Q: Determine the surface area generated by revolving the curve y=-x'over the interval 3 [0, 2], about…

A: The surface area of revolution of y=fx over a,b revolved about x-axis is A=2π∫abfxdfdx2+1dx Now, we…

Q: Compute the surface area of revolution about the x-axis over the interval [3,6] for y = 4x + 4. (Use…

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Q: Evaluate the volume of the surface of the shaped recreated by revolving the line y = 1/x as x goes…

A: Solution is written in below steps.

Q: Compute the surface area of revolution about the x-axis over the interval [2, 4] for y = 4x + 5.…

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Q: Compute the surface area of the solid obtained by revolving the region between the x-axis and the…

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Q: Find the area of the surface generated by revolving the curve y /2x-x, 0.25 sxs1.5, about the…

A: Use surface area formula about x asis

Q: Find the area of the surface formed by revolving the graph of f (x) = x³ on the interval [0,1]…

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Q: Find the surface area give y^2 +4x =2lny, 0, 0≤y≤3  ; about the  x-axis.

A: We have to find the surface area give y2 + 4x = 2lny , 0 ≤ y ≤ 3 ,  about the  x-axis.

Q: Find the area of the surface formed by revolving the graph y=x on the interval [0,3] about x-axis.

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Q: Find the surface area of revolution of x=y2 about the y-axis at [0,2]. Graph.

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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 surface area generated by revolving y=7x+6 about the x axis on the interval [0,6]

A: We need to find the surface area generated by revolving y=7x+6 about the x axis on the interval…

Q: Find the surface area generated by rotating the curve f(x) = 6 – 2x, 1 < x < 3, about the x-axis.

A: We first find the derivative of the given function

Q: Find the surface area of the solid generated by revolving the region bounded by the graphs of y =…

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Q: Find the surface area of revolution about the x-axis of y = 7 sin(3x) over the interval 0 < x <

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Q: Compute the surface area of revolution about the x-axis over the interval [3, 5] for y = 2x + 4.

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Q: Find

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Q: Find the surface area of revolution about the x-axis of y=3sin(7x) over the interval 0≤x≤π

A: To find the surface area of revolution about the x-axis of y=3sin(7x) over the interval 0≤x≤π.

Q: Find the area of the surface obtained by rotating the curve y=sqrt(4x) from x=0 to x=6 about the…

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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 surface area of revolution about the x-axis of  y= 4sin(4x), from x is greater than or…

A: Equation of curve is y= 4sin(4x) The interval is 0≤x≤π2

Q: Find the volume of the solid cut from the first octant by the surface z=4-x2-y.

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Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: Q3: Calculate the volume of the solid obtained by rotating the region bounded by the curve y = 2x -x…

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Q: Compute the surface area of revolution about the x-axis over the interval [8, 5e] for y = x² -…

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Q: Determine the volume of the solid of revolution which is formed when the enclosed region between…

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Q: Compute the surface area of revolution of y=sinx about the x-axis over the interval [0,π].

A: Given data: The expression for the given function is y=sinx. The given interval of x is [a,b]=[0,…

Q: Find the surface area of revolution about the x-axis of y = 2 sin(2x) over the interval 0 ≤ x ≤ KIN

A: When a cut= when a curve y=f(x)  a≤x≤b  rotate about x axis then surface area of rotation Ax=∫ab2πy…

Q: Find the surface area generated by revolving y=5x+2 about the x axis on the interval [0,6]

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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: the x-axis of y=2sin(4x) over the interval 0≤x≤π4

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Q: Find the area of the surface that is obtained by rotating the graph of X = 1+ Y² (Y = 1 to Y= 2)…

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Q: Find the abscissa of the centroid of the region between the parabola y = 6 − x2 and the line y = 1 −…

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)=8x$ on the…

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Q: The area under the curve 4y2 =" (x2 + 1)3 was rotated about a line located to the left of y – axis…

A: The surface area of the solid can be obtained using the Pappus theorem. The surface area is…

Q: Find the area of the surface formed by revolving the graph of y = 2Vx on the interval [0, 14] about…

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Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

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Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: Find the area of the surface that is obtained by rotating the graph of X = 1+Y² (Y = 1 to Y= 2)…

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Q: Find the volume and the surface area that generated due to rotate the bounded area between the curve…

A: I use washer method to find volume about x axis

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.