Find the surface area generated by revolving the portion of the curve y=x^2+1 between x=1 and x=2 about x-axis.

Q: What is the volume of the solid that results when the region enclosed by the curves y = cosx and y =…

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Q: Find the area of the surface formed by revolving the graph of f (x) = x2 on the interval [0,√2]…

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Q: Determine the area of the region between the two curves by integrating over .the y-axis X = y2 and x…

A: Area of the region between the two curves x1(y)  and  x2(y) is given by ∫abx1-x2dy    where a≤y≤b

Q: Determine the surface area generated by revolving the curve y=1/3 x³ over the interval (0,2), about…

A: The given curve is y=13x3  on 0, 2. This implies that, dydx=x21+dydx2=1+x41+dydx2=1+x4y1+dydx2=13x3…

Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x and the…

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Q: Find the surface area of volume generated when the curve y=.5(x^2+1) from x=0 to x=1 revolves around…

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Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

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Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 4x³.

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Q: Compute the surface area of revolution of y=sinx about the x-axis over the interval [0,3π]. Surface…

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Q: Find the area of the surface obtained by rotating the curve y=4x3 from x=0 to x=2 about the x-axis.…

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Q: Find the surface area for the solid of revolutic -1< x<1 about the x-axis.

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Q: Compute the surface area formed by rotating the portion of the curve in the first quadrant about the…

A: Given curve is x=(cost)(1+cost),y=(sint)(1+cost) , 0≤t≤2π Differentiate with respect to t.…

Q: Compute the surface area of revolution about the x-axis over the interval [3,6] for y = 4x + 4. (Use…

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Q: Find the area of the surface generated by revolving the curve about the indicated axis. 1) y = √4x -…

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Q: Compute the surface area of revolution about the x-axis over the interval [2, 4] for y = 4x + 5.…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: Diameter=60 meters⇒radius=30 meters                         ∵Radius is half of the…

Q: Find an integral for the area of the surface obtained by rotating y = √25-x, 9 ≤x≤ 16, about the…

A: To find an integral for the area of the surface obtained by rotating the below equation about the…

Q: What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square…

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Q: Find the approximate surface area of a sphere of radius 3.02 in. (Use differentials)

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Q: Find the surface area of revolution about the x-axis of y = 3 sin(6x) over the interval 0 <x < -

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Q: Find the surface area give y^2 +4x =2lny, 0, 0≤y≤3  ; about the  x-axis.

A: We have to find the surface area give y2 + 4x = 2lny , 0 ≤ y ≤ 3 ,  about the  x-axis.

Q: Use either a computer algebra system or a table of integrals to find the exact area of the surface…

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Q: Find the area of the surface of the solid formed by revolving one arch of the parametric curve given…

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Q: Find the area of the surface generated by revolving the curve about the indicated axis.   y = x 2/4…

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Q: Find the area of the surface generated by revolving the curve about the indicated axis. SET UP ONLY…

A: The area of the surface generated by revolving the curve around the y axis can be given as:…

Q: Compute the surface area of revolution about the x-axis over the interval [3, 5] for y = 2x + 4.

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Q: Find the moment of inertia of the area bounded by the curve x^2=8y, the line x=4 and the x-axis on…

A: Use moment of inertia concept

Q: Find the surface area generated by revolving about the y-axis that part of the curve y = In x lying…

A: Solution We have to find the Surface area generated by revolving about the y-axis the part of curve…

Q: Find the surface area of revolution about the x-axis of y=3sin(7x) over the interval 0≤x≤π

A: To find the surface area of revolution about the x-axis of y=3sin(7x) over the interval 0≤x≤π.

Q: Find the area of the surface obtained by rotating the curve y=sqrt(4x) from x=0 to x=6 about the…

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Q: Use differential to calculate the volume of the material needed in making a thin sphere with inner…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: find surface of patin Jenerated yースニュ0cx」 area revalving eurve 2. about メ~axis.

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Q: Compute the surface area of revolution about the x-axis over the interval [8, 5e] for y = x² -…

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Q: : Find the volume of the solid generated by revolving the shaded region about the x-axis: y = sinx…

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

A: Given data: The expression for the given function is y=sinx. The given interval of x is [a,b]=[0,…

Q: Find the surface area of revolution about the x-axis of y = 2 sin(2x) over the interval 0 ≤ x ≤ KIN

A: When a cut= when a curve y=f(x)  a≤x≤b  rotate about x axis then surface area of rotation Ax=∫ab2πy…

Q: Find the area of the surface obtained by rotating the curve about the y-axis. y= x², 0sxs1 Set up…

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Q: Compute surface area of revolution about the x-axis over the interval (0, pi) for y= 6sin(x)

A: Surface area of curve revalue aroundx-axis is given by,S = ∫ab2π y 1+dydx2 dxa,b is the interval.

Q: Compute the surface area of revolution about the x-axis over the interval [3,6] for y = 2x + 5. (Use…

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Q: Find the moment of inertia with respect to the y-axis of the area bounded by the curve y=1-x3 and…

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Q: The area under the curve 4y2 =" (x2 + 1)3 was rotated about a line located to the left of y – axis…

A: The surface area of the solid can be obtained using the Pappus theorem. The surface area is…

Q: 12. Informally explain how a surface area generated by a curve of rotation can be computed with an…

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Q: Find the area of the surface formed by revolving the graph of y = 2Vx on the interval [0, 14] about…

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Q: What is the differential form for the total surface area of a frustum of a cone with l as the slant…

A: The curved surface area of a frustum of a cone is:

Q: Approximate the change in the lateral surface area (excluding the area of the base) of a right…

A: To approximate the change in the lateral surface area: We  can approximate the change from  a  to…

Q: Find the area of the surface obtained by rotating the curve y = about y-axis for 1 ≤ y ≤ 3. Area:

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Q: Find the surface area generated by revolving the parabolic arc y=x² , Osxs6 around y-axis

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Q: Find the area of the surface generated by revolving the curve x = Osys2, about the y-axis

A: Given: The curve is x=y32, 0≤y≤2 about the y-axis The formula for find the area of the surface is…

Q: Compute the surface area of revolution about the x-axis over the interval [3, 6] for y = 4x + 5.…

A: The equation of the curve is given by y = 4x+5 Formula Used: S = 2π∫36y1+dydx2dx To evaluate: The…