The area of the surface obtained by revolving the curve Vy+1 for a-1.) 2л. dy 4y +4 a b. TV4Y +5 dy a b. 2n Vy+1 dy a T(y + 1)2 dy

Q: Consider the surface obtained by revolving the line y=2-x 0<x<2 around the x-axis. Which of the…

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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: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. Ex + 9…

A: According to the given information it is required to evaluate the integral using green’s theorem.

Q: Set up an integral for the area of the surface generated by revolving the given curve about the…

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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: Which of the following integrals represent the area of surface obtained by rotating the curve y= =…

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Q: The area of the surface obtained by revolving the curve x= Vy+3 for a-3.) 2x /4y + 12 dy 2л уу +3 dy…

A: Consider the curve x=y+3 for a≤y≤b. Find the area of surface when curve is rotated about y-axis.…

Q: The surface area of the solid generated by revolving the straight line 2y = x+1 bounded by x-1, x 3…

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Q: The surface formed by rotating the curve y = x 2 1, about the x-axis is known as Gabriel's horn.…

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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 moment of inertia about the​ x-axis of a thin plate bounded by the parabola x=2y-3y2 and…

A: Given that the equation of the parabola,x = 2y – 3y2and the equation of linex + 7y = 0

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

A: Use Green Theorem to evaluate  ∫C5y+9exdx+10x+7cosy2dy where, C is the boundary of the region…

Q: 3. Find the volume of the solid formed by revolving the region formed by the curve y = sec about the…

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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: 2.) Set up and evaluate the definite integral for the area of the surface generated by revolving the…

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Q: Find the center of mass of a thin plate covering the region between the x-axis and the curve y =…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

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Q: Set up the integral for the Surface Area of the curve witn given rotation: 1 from ( 2) to (1, 1)…

A: Given curve is x=1/y2 IInterval is (1/4,2 ) to (1,1)

Q: The base of a lamp is constructed by revolving a quarter circle  y = (2x-x^2)^0.5  around the…

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Q: Set up the integral for the Surface Area of the curve y = In(x) from (1, 0) to (e, 1) %3D rotated…

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Q: Set up and simplify the integral that gives the surface area of revolution generated by rotation of…

A: Given; y=x-x^2, 0≤x≤1

Q: The area of the surface obtained by revolving the curve y = x² , for 1<x<2 , about the y- axis, is…

A: we will select a disc inside of thickness dy and radius xy will vary from 1 to 4circumferene of the…

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: 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: 5. Compute the volume of the solid obtained by revolving the curve y = vx sin x about the x-axis…

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Q: Set up an integral for the area of the surface generated by revolving the curve y = x2 about the…

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Q: Which of the following integrals gives the area of the surface obtained by 3 rotating the curve y…

A: Solution: The objective is to determine which of the following integrals gives the area of the…

Q: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

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Q: The area of the surface generated by rotating the curve y = 2 + e*, where 1 < x < 2, about the…

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Q: The area of the surface obtained by revolving the curve x Vy+3 for as-3.) n(y +3) dy 1+ 4y + 12 dy…

A: Explained below

Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

A: given curve y=2x over the interval [4,9]

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: Compute the surface area of revolution of f (x) (x + 1)z about the x-axis over 3 [0,1]

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Q: Set up an integral to find the area of the surface generated by rotating the curvey= 4ln x, from x =…

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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: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A: y=16-x2,  -1≤x≤1 Differentiating with respect to x, we get…

Q: 15 Find the area of the surface generated by revolving x = 4/4- y,0sys about the y-axis. x=4/4-y Set…

A: find the area of the surface  generated by revolvigx=44-y, 0≤y≤154about y-axis

Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: 2. Determine the area of the surface generated by revolving a given curve about a given axis. a.…

A: Formula to find the surface area by revolution helps to find the required surface area. Formula to…

Q: set up an integral that representsthe are of the surface obtained by rotating the curve x=2t2+1/t…

A: To determine the integral representation of the area of the surface that is oriented by rotating the…

Q: Find the area of the surface generated by revolving the curve x = 4 1 from 8y 3 < y< 5 about the…

A: When a function is of the form x=g(y) and you are revolving around the x-axis, the interval is c≤y≤d…

Q: ху — 4, 1 <x< 8

A: Surface area.

Q: Use either a CAS or a table of integrals to find the exact area of the surface obtained by rotating…

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Q: 8. Find the area of the surface of the region generated by rotating the curve y = x³ from x=0 to x=1…

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Q: 6. Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: compute the surface area of revolution about the x-axis over the interval. y = (4 − x2/3)3/2, [0, 8]

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Q: compute the surface area of revolution about the x-axis over the interval. y = x, [0, 4]

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Q: Given x= In(2y+1), 0<y<l. a) Set up an integral for the area of the surface obtained byrotating the…

A: The curve given is as follows: fy=x=ln2y+1,  0≤y≤1 (a) Differentiate the function.…

Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

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