Find the surface area generated by rotating the first quadrant portion of the curve  x2=16-8y about the y-axis.

Q: find the exact area of the surface by rotating the curve about the x-axis  Y=x^3  0<x<2

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Q: Find the area of the surface obtained by rotating the curve y=1+4x^2 from x=0 to x=7 about the…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. X = =…

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 2(x² -…

A: Above question is solved.

Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x, 0 <xs;…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V5 - x, 3 <…

A: Definition used -                             Area of the surface obtained by rotating the curve…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √ 1 + ex,…

A: We need to find Surface area.

Q: Find the area of the surface generated by revolving the curve y = 2Va, 0 <x < 3, about the x-axis.

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Q: Find the area of the surface obtained by rotating the given curve about the indicated line, y=x,…

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Q: 6. Find the surface area generated by rotating the first quadrant portion of the curve y = 9 – x2…

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 4(x² −…

A: When a curve  described by the function x=g(y), a≤y≤b  rotated about the y−axis, Then the area of…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 y = + /- 2x

A: Given: The equation of the curve y=x36+12x,where  12≤x≤1. Calculation: Compute the surface area as…

Q: Find the exact area of the surface obtained by rotating the given curve about the y-axis.

A: Given that      x(t)=3t-t3y(t)=3t2 Since, we are rotating about y-axis, the formula is:…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + ex,…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V6 - x, 4 <…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V6 - x,…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √7-x, 1 ≤x≤7

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = sqrt 1+3x ,…

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² -…

A: The given curve is y2=9x2-a2 in the first quadrant. We need to find the surface area when the given…

Q: Find the area of the surface generated by revolving the given curve about the x- axis: y = 19 – x²,…

A: Given,y=9-x2   squaring both the sides,y2=9-x2x2+y2=9x2+y2=32this is the equation of the circle with…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √ 1 + ex,…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x St, y 2t, 0st…

A: Given that        x = 5t , y = 2t  , 0 &lt;= t &lt;= 5  Here we have to find the area of the surface…

Q: Find the area of the surface obtained by rotating the curve y 4V7,0 < I < 5, along the r-axis.

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Q: Determine the surface area of revolution when the curve y = 7.2/x from x = 1 to x = 5 is rotated by…

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Q: y = V8 - x, 2 <x S 8

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Q: Find the area of the surface obtained by rotating the curve I = 3t y = 3t, 0<t< 1 about the r-axis.…

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Q: Find the area of the surface obtained by rotating the curve y = √(5-x),   3≤x≤5 about the x-axis.

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Q: Find the area of the surface generated by revolving the curve - 5x y = e-b", x > 0 around the -axis.

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Q: Find the area of the surface generated by revolving the curve - 5x y = e x > 0

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = 1 1sxs1 2x'…

A: The given curve is  y=x36+12x

Q: Find the area of the surface obtained by rotating the curve y = 2x 223 from x = 0 to x 2 about the…

A: HERE THE LIMITS OF INTEGRATION IS 0 to 2.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + ex,…

A: Given curve is y=1+ex and we have dydx=ex21+ex Since the Area of the surface obtained by rotating…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y= square root…

A: The given curve is

Q: Find the area of the surface obtained by rotating the curve y=1+3x² from 0 to x = 9 about the…

A: Let's find area of surface obtained by given curve.

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 2(x² −…

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Q: Find the area of the surface generated by revolving the curve y =,0sx<2, about the x-axis.

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Q: Find the area of the surface generated by revolving the curve Y = 8/x, 2 < x < 7 around the -axis.

A: The given surface is generated by y=8x,  2≤x≤7 around the x axis. The area of the surface generated…

Q: Find the area of the surface obtained by rotating the curve y=1/33/2, 0 ≤ y≤12  about the y - axis.

A: To find the area of the surface obtained by rotating the curve

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y =

A: Given curve is  y=x36+12x Differentiate with respect to x. dydx=x22-12x2

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + 5x,…

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Q: Find the area of the surface generated by revolving the curve about each given axis. X = 9t, y = 9t,…

A: Solution

Q: Find the area of the surface obtained by rotating the curve y=1/3 x3/2, 0≤y≤12  about the y- axis.

A: Let a rectangular strip parallel to x-axis of thickness dy be made whose tip touches the curve…

Q: EX- Find the area of the surface generated by rotating the 1 portion of the curve y= (x²+2)³ between…

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Q: "ind the area of the surface generated by revolving the curve x = 2/1- y, –1< y <0 bout the y-axis.

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + e*, 0 <…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x, 0< x< 5

A: Surface area of given curve after rotation about x axis.

Q: Find the surface area of the portion of the curve x2 = 4y from y = 1 to y =2 when it is revolved…

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Q: Find the area of the surface generated by revolving the curve y = 3/x, 1 < x <4 about the x axis.

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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.