Find the area of the surface obtained by rotating the curve x = 20 cos° 0, y = 20 sin 0, 0

Q: The curve y= sinh x, 0< x <9 is revolved around the x-axis. Find the area of the resulting surface.…

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Q: 3. Find the area of the surface generated by revolving about the y-axis the part of the curve y = x?…

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Q: Find the area of the surface generated by revolving the curve x= cos (3t), y = 5+ sin (3t) on 0sts,…

A: Suppose parametric curve rt=xt,yt for a≤t≤b are revolving about the x-axis then surface area…

Q: Find the surface area for x=3( θ – sin θ ) , y= 3(1-cos θ ). , when rotated along the x axis.

A: Given x=3θ-sin θ,  y=31-cos θ  The surface area is rotated along the x-axis. Then y=0, 31-cos…

Q: Find the surface area generated by rotating y=sin x. 0 ≤ x≤ π about the x-aixs.

A: Area of surface problem....

Q: (b) Use Simpson's Rule with n = 10 to estimate the area of the surface obtained by ro the cosine…

A: I have solved b part as asked.

Q: 1(b) Find the surface area generated by revolving the portion of the curve y x2 + 1 between x=0 and…

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Q: (b) Use Simpson's Rule with n = 10 to estimate the area of the surface obtained by rotating the sine…

A: Let's solve area of surface.

Q: Find the area of the surface generated by revolving the curve a. y = V1+ e* between x = 0 and x = 1…

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Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: T X =…

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Q: 16 The area under the curve 4y? (x2 + 1)3 was rotated about a line located to the left 9 of y – axis…

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

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Q: Find the area of surface revolution, when x=1+cosθ. , y=sinθ Where 0≤θ≤2π

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Q: Find the area of the surface obtained by revolving the given curve about the x-axis. on (0, In(3)

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Q: cos(2t), y = 4+ sin(2t) 0 <t< on 2

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Q: Find the area of the surface generated by revolving the curve a. y = V1+ e* between x = 0 O and x =…

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Q: Find the area of the surface generated by revolving the curve x = a cos θ,       y = b sin θ, 0 ≤ θ…

A: The curves x=acosθ,y=asinθ, and 0≤θ≤2π, we have to find the area of the surface generated by…

Q: Find the surface area of the object obtained by rotating y = sin(2x) , 0<x< about the x-axis.

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Q: Find the area of the surface generated by revolving the curve y = cos(x), 0 < x<: about the r- axis.

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Q: Find the area bounded by the parametric curve x = cos(t), y = e', 0<t< 1/2, and the lines y = 1 and…

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Q: Find the area of the surface generated by revolving the curve x = 2 cos θ,       y = 2 sin θ,   0 ≤…

A: If x=f(t), y=f(t) then surface area is, About x axis: S=2π∫abydxdt2+dydt2dt About y axis:…

Q: Find the area of the surface generated by revolving the parametric curve x = cos² t, y = sin² t (0 ≤…

A: To find: The area of the surface generated by revolving the curve about y-axis. Given: The…

Q: Find the area of the surface generated by revolving the curve about the indicated axis. y = V, 0,5 s…

A: First I have written the formula of are of surface of revolution about y axis on an interval, just…

Q: The given curve is rotated about the y-axis. Set up, but do not evaluate, an integral for the area…

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Q: 1. Find the area of surface that is generated by revolving the portion of the curve y = V4- r2…

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Q: Determine the area under the parametric curve given by x = 2(0 sin 0), y = 2(1 - cos 0), 0≤ 0 ≤ 2π.

A: I have given the answer in the next step. Hope you understand that

Q: Find the area of the surface generated by revolving the curve defined by x(t) = 3 cos t, y(t) = 3…

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Q: Find the area of the surface generated by revolving the given curve about the indicated axis. 1. x =…

A: Consider two parametric equations and with . Then the area of the surface obtained by rotating…

Q: Find the surface area of the surface generated by rotating y = cos x, 0 ≤ x ≤ π/2, about the x-axis.

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Q: Find the area of the surface obtained by rotating the given curve about x-axis. x=cos (t),…

A: We have to find the area of the surface obtained by rotating the given curve about the x-axis. x=cos…

Q: Find the area enclosed by the given parametric curve and the x-axis. x = 2 sin(t),  y = sin(t)…

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Q: Find the area of the surface generated by revolving about x-axis the part of the curve y = sin x,…

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

A: We have given the function; We know the formula for surface area by revolution;

Q: Find the area of the surface generated by revolving the curves about the indicated axis. 5) x = sin…

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Q: Find the area of the region bounded by the parametric curve x = e³¹, y = e²¹ and the X- axis on the…

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Q: Let x=sin^2t, y=cos^2t. 0</=t</=pi/2  Find the surface area about x-axis

A: Given, x=sin2 ty=cos2 t 0≤t≤π2 We have to find surface area about x-axis. Chain rule for…

Q: 3) Find the area of the surface that results from rotating the curve Y = sin MX, 0 s X < 1 about the…

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Q: Find the exact arc length of the curve 2xy = y² + 4 over the interval 2 ≤ y ≤ 4. Find the area of…

A: Given: 2xy=y2+4 over 2≤y≤4 to find the arc length of the curve and given the another equation is…

Q: Find the area of the surface obtained by rotating the curve about the x-axis. Recall: S=2n |…

A: Find the surface area

Q: 1.Find the exact area of the surface obtained by rotating the curve about the x-axis. y = 4 - x, 1…

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Q: Find the exact arc length of the curve over the interval 24xy = y* + 48 from y = 2 to y = 4 . Eind…

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

Q: Find the area of the surface generated by revolving the curve x = Vy, over the interval 8 sys 27…

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

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Q: Express the area of the surface obtained by rotating the curve y =In sec(2x) between x = 0 and x =…

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Q: Find the area of the surface of revolution obtained by rotating the function y=sin(x) on the…

A: Here is the given curve and the interval it is bounded by: y=sin(x) interval {0,pi} about the x…

Q: Find the area bounded by the parametric curve x=cos(t),y=et,0≤t≤π/2, and the lines y=1 and x=0.…

A: Given: x=cost,y=et, 0≤t≤π2

Q: The surface area obtained by rotating the parametric curve X= e° + e=t, y= 5-2t about the y-axis…

A: We need to find the derivatives of x and y with respect to t dxdt =d et + e-tdt = et  - e-t dydt =…

Q: need help solving the equation below

A: From the given information it is required to calculate the exact area of the surface obtained by…

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.

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.