The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 5 sxS 21

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A: We have to find  the surface area generation by revolving the curve about x and y axis

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A: Given: x=t ; y=4-2t; 0≤t≤2To find the area of the surface generated by revolving the curve about…

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Q: Find the area of the surface generated when the indicated arc is revolved about the y-axis. DRAW A…

A: Introduction: When an arc is revolved around the coordinate axis, a solid is formed. This solid has…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y =x2 4 In(x),…

A: Given curve is y=14x2-12ln(x) Differentiate with respect to x. dydx=x2-12x

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Q: The given curve is rotated about the y-axis. Find thearea of the resulting surface.   y = 1 -x2…

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Q: |Find the average distance from the origin over all the points in the unit circular disk 2² +y? <1.…

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Q: Find the area of the surface generated when the indicated arc is revolved about the y-axis. Draw a…

A: For the solution of the problem follow the next steps.

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 3sy54

A: Given:y=x3  ,     3≤y≤4Surface area :S=∫ba2πx 1+dxdy2   dy

Q: x² : 4ay from x 0 to x = 2a

A: We have to compute the surface area of revolution of the curve x2=4ay about the y-axis between the…

Q: Find the area of the surface generated when the indicated arc is revolved about y-axis x^2 = 4ay…

A: Surface area about  y-axis is given below..

Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

A: Given   Area of surface area revolved about x axis formula is

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A: given

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A: Given, R=12 ∮∂Rxdy-ydx From the given figure on ∂R we have, rt=acosti^+bsintj^ that is on ∂R,…

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Q: Find the area of the surface obtained by revolving the curve y=2/4=x, for 1<«<4, around the x-axis.…

A: Explanation of the solution is given below...

Q: 1/B) Find the length of the cardioid 'curve: r = 1 + cose

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y=x3 + for…

A: surface area of the curve is given by  S=2π∫abf(x) (f'(x))^2+1 dx

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y 10x…

A: Given:

Q: c) Find the curve length of the lemniscate of the area Inside the lemniscate r² = 6 cos 20 and…

A: Solution:-

Q: Question 7 Find the area enclosed by the curves y=2r², y=2\/x,x=- and x = 1 A 45/51 B 59/76 49/96…

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Q: What r and h gives the cone with the largest amount of waffle material? Tp²h 3 Let S = surface area.…

A: There are multiple question , as per company policy kindly ask other question separately. Given

Q: Find the area of the specified region. Shared SE by the circle r= 5 and the cardioid A) B) = 5(1+…

A: This problem is related to application of integration

Q: 3) çalculate Sſ e-(x<+Y²) dA on D which is the region in the first quadrant bounded by the circle X²…

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Q: Find the area of the surface generated when the given curve is revolved about the y- axis. y =, for…

A: Answer is optional B

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

A: Area of surface generated by a curve y=f(x) when revolved around y -axis  S=∫ 2πx dsWhere…

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

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Q: Question 2: Find the surface area of the object by rotating y = 4 + 3x² , 7< y < 16 about the…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 0SxS 12

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Q: Question 8 Calculate the area of the surface generated when the curve, y = Vx is revolved on the…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. 1 In(x), 4< x <…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = ? - Incx),…

A: Given that: y=14x2-12ln(x),     2≤x≤5

Q: Q. The curve y = v4 – x², -1 <x<1, is an arc of the circle x? + y? = 4. Find the area of the surface…

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Q: -y° dr + x* dy where C is the union of the circles of radii 1 and 2 (centered at the origin).

A: Let I=∮C−y3dx+x3dy According to green theorem ∮CLdx+Mdy=∬D∂M∂x−∂L∂ydxdy Where, D is the region…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = =x² - 1 1,2…

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Q: Find the area of the surface generated when the indicated arc is revolved about the y-axis: a. y =…

A: Given :y=2xx=0 to x=4

Q: Question 7 Find the area enclosed by the curves y=2x², y=2√x,x= — and x = 1 A 45/51 B) 59/76 49/96…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis 1 = (e…

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Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8ry? = 2y® +…

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Q: The accompanying figure shows a spherical cap of height h cut from a sphere of radius r. Show that…

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Q: ) Let D be the region located in the first quadrant of R² between the two circles of radii 1 and 4…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the surface area generated by revolving one arc (first quadrant) of y = cos x about the x-axis.…

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Q: Consider the curve y = 3 sin(2x), where 0 < x < T/2. Find the surface area when this curve is…

A: To find the surface area when the curve the is rotated about the x-axis.

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

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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.