Find the area enclosed by the curve ax =y(2a– y).

Q: Calculate the integral O (y – e*) dx + (3x + e') dy where L is along the curve x + y´ : = /x2 + y² -…

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Q: Evaluate the line integral y dx +xdy; C is the curve x = 4t, y = t³ – 1, 0sts 1. Jy dx + x*dy (Туре…

A: Consider the provided question,

Q: Find the area of the closed region enclosed by the curve defined parametrically by x = 4 cos t, y =…

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Q: Calculate the integral xy² dy – x²y dx where L is along the curve x + y ² = a? (a > 0) in a…

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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: Evaluate the double integral. 7xy dA; R R is the region in the first quadrant enclosed by y = Vx,y =…

A: We have to find the ∬7xydA

Q: Evaluate I Jx2 + y2 dV where B is the region lying above the xy-plane, and below cone z = 16 – Vx² +…

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Q: HW: Find the area of the surface generaled by revolving 1. Vy, 1 <y <8 about the x- axis. =DX

A: Find the attachment

Q: Q3/A/Find the surface area generated by rotating the curve y = cos h(x) about x axis for 0≤x≤1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: f(x) = x³, with 0 < x < 1

A: We know, the surface area of the solid that is obtained by rotating the graph of y=f(x) about the…

Q: Find the surface area of the surface attained by revolving the curve y = f(x) = r' around the x-…

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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: Find the area bounded by the parametric curve x=t−(1/t), y=t+(1\t) and the line y=2.5.

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Q: Evaluate the integral ∫Cydx−xdy over the curve C parameterized by r(t)= (cost,sint), 0≤t≤π2.

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Q: x dy - y dx

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Q: Find the area of the surface generated by revolving the C = ((x, y): x = 3 (t – sin t), y = 3 (1-…

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Q: Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 x} | about the x-axis.

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Q: c) Find the surface area generated by rotating the curve y = (x²+2)³/2, 0≤x≤3 about the y-axis.

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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: Evaluate the double integral / |: xy dA where D is the region bounded by the line y = x – 1 and the…

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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: Set up an integral for the area of the surface generated by revolving the curve y=x about the…

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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: Evaluate (x+ y) dx +xy dy, where Cis the positively-oriented boundary of the region bounded by the…

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Q: Solve for the area of the portion of the cylinder x = /1 – y², which lies between the planes z = 0…

A: Here is the solution of the given problem:  By using line integral to find the surface area of…

Q: Find the moment of inertia of the area bounded by the parabola y^2 = 4x, x-axis, and the line x = 1,…

A: Given

Q: E valuate the bounded by the area parabola X = - y f the line y=xt2

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Q: I = (4xy' + (y')²)dx

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Q: a) Find the surface area of the object obtained by rotating x = e2y , –1 <y <1 about the y – axis.

A: We have to find the surface area of the solid obtained by rotating the curve x=e2y about the y-…

Q: 1+y dy

A: We can solve the given integral as follows:

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

A: If x=x(t) and y=y(t) then surface area of the region rotating about y-axis is given by…

Q: Evaluate the double integral I|. (10z + y) dA where Ris the region between the curves a? + y? = 12…

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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: Find the center of gravity of the region bounded by the x-axis, the curve y = sec x, and the lines x…

A: Consider the given question,The graph of the curve y = sec(x) and the line x = -pi/4, x = -pi/4 is…

Q: Calculate the integral of C being the curve given below. y= 3+x y= 3-x 6x dS C

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Q: Find the area of the Surface generated by revolving the given curve about the - axis while x is over…

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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: 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: The area enclosed by the curve y = Va and y = x is given by: x – a², y – y° dy x dx - y? – y dy

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Q: Find the area of the surface generated by revolving the curve x = 6t , y = 4t2 for t = 0 to t = 1…

A: Differentiate the equations x=6t and y=4t2 with respect to t, to find dxdt and dydt.…

Q: Find the area of the surface obtained by rotating the curve y = Vx on the interval [0,1] around the…

A: The equation of the curve is y = x3 = x13 To evaluate: The area obtained by rotating the curve on…

Q: find the area of the surface formed by revolving the cardioid r= a(1+cosθ) about the x-axis

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Q: the surface area generated by revolving c(t) = (cost,sint) about the y-axis for 0 ≤ t ≤ π 2.

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Q: Compute the surface area of the cone generated by revolving the curve c(1) = (1, mt) about the…

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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: Set up an integral that represents the area of the surface obtained by rotating the curve = e2t, y =…

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Q: Find the area bounded by the line y=4 and the curve described parametrically by: x(t) =…

A: Given: y=4x(t)=t-1t,    y(t)=3t+1tSince y=4,  y(t)=3t+1t ⇒ 3t+1t=4⇒3t2-4t+1=0⇒3t2-3t-t+1=0…

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: Find the exact area of the surface obtained x=t°, y =t 0<t<lby rotating about the x- аxis.

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