Find the exact area of the surface obtained x = t°, y =t" 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: Find the area of the surface generated by revolving the curves about the indicated axis. A) 247? B)…

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Q: Find the area enclosed by the ellipse x = a cos t, y = b sin t, 0 ≤ t ≤ 2π.

A: Given Data The first equation of ellipse is x=a cos t. The second equation of ellipse is y=b sin t.…

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

Q: For the curve y = x^2 + 1 between the points (1,2) ??? (3,10) : a. find the Arc Length b. and find…

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

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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: 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: The sphere of radius a centered at the origin is expressed in Cartesan coordinate as x +y² +z? = a².…

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Q: Find the surface area generated b rotating the portion of the parabolic arc x = y^2 from x =0 and x…

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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 generated by revolving the C = ((x, y): x = 3 (t – sin t), y = 3 (1-…

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Q: Find the area of the surface generated by revolving the curve 6a² xy = y + 3a from y= a to y = 3a…

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

A: We have to check which curves would generate equal surface area revolved around x and y axis.

Q: Use polar coordinates to find the integral 16 - x² - y? dx dy where R is the circle x? + y? < 4.

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Q: Find the surface area of a sphere of radius r using the formula of arc length with respect to x.

A: The objective is to find the surface area of a sphere of radius r using the formula of arc length…

Q: y? - In(Vy), 1sys 5 about the x-axis is The area of the surface obtained by rotating the curve x =

A: Solve the following

Q: Use integration and trigonometric substitution to find the area enclosed by the ellipse: x² y? = 1.…

A: From the given ellipse: x24+y216=1 So, x24+y216=1x-0222+y-0242=1center:(h,k)=(0,0)Major-axix &amp;…

Q: a. Use integrals to show that the circumference of the circle x2 + y? a? is 2na. %3D b. Find the…

A: Solving question (a),

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

A: Given the curve, 8xy2 = 2y6+1,  1≤y≤2 we have to find the area of the surface generated by revolving…

Q: Find the surface arca of y = (1/3)r 10<x <1 revolved about the z-ax

A: Given: The equation is y = 13x3 , 0 ≤x≤1 revolved about the x - axis.

Q: Find the surface area of the portion of the sphere of radius 4 that lies inside the Fylinder x2+y? =…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The integral /4x? + 4y? + 42² dV тп, R where R is the solid hemisphere with x? + y? + z² 0 Find the…

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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: 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…

Q: Find the equation to solve the surface area obtained by revolving the parabola x? = 4y from x = -2…

A: If is a function, then the independent variable x is called the input of the function and the…

Q: Show that the surface area obtained when the arc of the parabola y? = 16az from I = 0 to r = h is…

A: Surface area

Q: Consider the parameterization for the cycloid given as: x = 4(1– sint) y = 4(1-cost) 0<t<2n a) Find…

A: Given curve is x=4t−sint and y=41−cost, 0≤t≤2π (a) We have to find the area of the arch of the…

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 surface generated by revolving x = e'cost, y = e'sint, 0 <t < about the x-axis,…

A: We’ll first need the derivatives of the parametric equations:

Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy? = 2y6 +…

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

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Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy? = 2y6 +…

A: We need to find the surface integral.

Q: Find the length of the radius r of a right circular cone with l = 12 in. and h = 3r in.

A: The circular cone described in the question is cut through the center and the triangle cut out is…

Q: Find the area enclosed by the ellipse x = a cos t, y = b sin t, 0&lt;= t&lt;= 2pai.

A: Given,

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

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Q: Find the area enclosed by the given ellipse. x- a cos t, y = b sin t, 0sts 2r

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

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Q: Jind the Surface area of the part of the para boloid 2=X+y" lyrng Orer the regron R

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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: y = 2(1+cos( Ɵ)) Find the area of the surface of revolution formed by rotating the upper half of…

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Q: (2) Evaluate the integral. Va? + y² dA; R: 4 < a² + y² < 9 (b) || sin(x? + y²) dA; Risa disk with…

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Q: Determine the surface area generated when a portion of the curve in the first quadrant of x2 y? = 1+…

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 when the indicated arc is revolved about the y -axis. 6. y =…

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Q: Prove that the surface area of a sphere with radius r is given by S = 4r? using the methods of this…

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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: 73. х %3D а сos'0, у%3Dasin'0, 0<0< п/2 0 < 0 < T/2

A: Given information: x=acos3θy=asin3θ0≤θ≤π2

Q: I = Examine the given integral dz ;C z-i -|= 2 the circle

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Q: Given the area bounded by the parabola x– 4x + 12y - 20 = 0, the x-axis and the lines x = 1 and x =…

A: ∫ (y^2)dx is the formula for moment of inertia