: The area of the surface obtained by rotating the curve y = 2 In a, for 1 < a

Q: The area of the surface obtained by revolving the curve y = x3 for 1<x<8 about the y-axis, is given…

A: Surface area obtaining by x=f(y) from x=a to x=b is about y-axis given in step 2.

Q: a) Calculate the arc-length of the curve y = In(1 – x²), between 0 <x< 1/2. %3D b) Find the area of…

A: Find the Arc length and surface area

Q: Under what conditions can you find the area of the surface generated by revolving a curve x = ƒ(t),…

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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 e + e -y revolving the curve x = 2 0sys In 6 about the…

A: To find the surface area generated by revolving the curve x=ey+e-y2,0≤y≤ln6 about the x-axis. We…

Q: nhuille Find the area of the rotaional L'C surface formed by rotating the part of the Curve given by…

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Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

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Q: Find the area of the surface obtained by rotating the curve y : sin x from x = 0 to x = 1.4 about…

A: Given region bounded by y= sinx  from x=0 to x=1.4

Q: Find the area of the surface generated by eY + e -y revolving the curve x = in the interval -In 2…

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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: Fi for oec ind volume of the solid of revolution by rolahng about the -ais each regton boundad b the…

A: To calculate the volume of the given solid of revolution

Q: Find the surface area of the curve: y In x; 1sx S 2 when the curve is rotated about the y-axis.

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Q: 9) Find the area of the surface generated by rotating about the y-axis y = x' between (0,0) and…

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Q: Use green's theorem to calculate the integral Fdr, F(r, y) = (e* + x²y , e³ – ry² + sen(3) + 2)…

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Q: 1. Find by integration the area of the surface of revolution generated by revolving the loop about…

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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: Where ds is calculated using the are length formulas from before (which ever is easiest)! 3. Find…

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Q: 21 Verify Green's theorem in the plane for the integral ${(x-y) dx- (+xy) dy} | where c is the…

A: Green's theorem for a plane states that if C is a closed curve inclosing a region D and u and v are…

Q: Find the area of the surface generated by revolving the curve, x = /6y – y? ; 2sys 5

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

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: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…

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Q: Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + (…

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Q: Which of the following is the surface area of the surface generated by revolving the curve y = 폴 in…

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Q: Find the area of the surface generated by revolving about the y-axis the arc C given by C = { (x,y)…

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Q: 1. Find the surface area of the solid obtained by revolving the curve y = √25-x from = 9 to x = 16…

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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 of the surface generated when the given arc is revolved about the y-axis ㄷ y = 4 - x²…

A: We have to find area of the surface .

Q: Find the area of the surface obtained by rotating the given curve about the x-a T x = 5 cos (0), y =…

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Q: Find the area of the surface generated by revolving the given curve about the y-axis from y = 0 to y…

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Q: 1. Find the area of the surface generated by revolving the given curve about the x-a (a) y = 7x,…

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Q: Find the area of the surface generated by revolving the curve x in the interval 2 Osys In6 about the…

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Q: The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3…

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Q: Let S be the surface area generated by revolving the curve y = Vx, 2 < x < 12 about the x- axis.…

A: This formula is used

Q: Evaluate the double integral // (x² + y² + 3) dA R over R: the circle centred at the origin (0, 0)…

A: Double Integration problem.....

Q: Evaluate the line integral L(a - )da + (1 + y° + æ")dy, where Cis the circle of radius 2 centered at…

A: We have to evaluate the integral.

Q: Evaluate the integral xy ds, where C is the curve consisting of the portion of the unit circle of…

A: The given integral is ∫Cxy ds where C is the curve consisting of the portion of the unit circle…

Q: Evaluate the integral | xy ds, where C is the curve consisting of the portion of the unit circle of…

A: Let us assume thatC1:x2+y2=1Put x=t,y=1-t2 and z=0.Hence,dx=dtdy=-t1-t2dz=0and 0≤t≤1.Let C2:The line…

Q: Find the area of the surface that is generated by revolving the portion of the curve yx' between x0…

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Q: Which of the following curves would generate equal surface area when revolved around x and y axes?…

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Q: Find the area of the surface generated by eY + e -Y revolving the curve x = in the interval 2 In 5…

A: solution:-given curve x=ey+e-y2 in the interval 0≤y≤ln5revolving about the y-axisarea of a surface…

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: Use green's theorem to calculate the integral Fdr, F(x, y) = (e* + a²y , e" – xy² + sen(y) + 2)…

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Q: Compute the line integral Sy?a dl where y is the part of the circle centered at the origin and of…

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Q: ind the exact area of the surface obtained by rotating the curve about the x y = y1+ ex, OsxS8

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

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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. y = v1+ ex, 0 <…

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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: The area of the surface obtained by rotating the curve y = et +e asxsb, about the x-axis is 1/2 e2 +…

A: Find the surface area rotating the curve about x axis

Q: 1. (a) Find the exact area of the surface obtained by rotating the curve y = e* 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. x = 5 + 4y2, 1 s…

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