3. Find the length of the curve y = x – In x, 1

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

Q: The area bounded by the curve z 4y+7, the y-ax y =0 and y 2 is dy3D O 18 22 11 O 15

A: Area bounded by the curve can be calculated as

Q: 10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

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Q: The area of the surface obtained by rotating the curve x = 1sys7 about the x-axis is

A: Definition used -              Area of the surface obtained by rotating the curve x=g(y) about…

Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

A:

Q: 7. Find the area of the surfaces generated by revolving the curve r = 2e®² for 0<0s- about x- axis.

A: The solution are next step..

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Q: 2. The surface area of the surface generated by revolving the curve y = x, -1 < x<1, about the…

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Q: Consider the region enclosed by the curves y = a2 +1 and y = 2r + 1:

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Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

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Q: 4. Graph the surface 1 = y² + z² by first sketching at least three cross sections in each of the 4…

A: We have to graph the surface 1=y2+z2-x24 by sketching at least three cross-sections in each of the…

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A:

Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = V3x +5…

A: Surface area of the bounded region along x axis

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A:

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: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = V3x +…

A:

Q: 4. Find the area of the surface generated when the given curve is revolved about the y-axis. y=(2x)"…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

A:

Q: 4. If the curve y = 3 – x², 0<x<4 is rotated about the y-axis, find the area of the resulting…

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Q: Find the length of the curve y =Vx³, for [0, 4]. Find also the surface area of the region is rotated…

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Q: Suppose that the curve y =( x^4)/8 + 1/(4x^2) on the interval [1, 2] was revolved about the x-axis.…

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Q: 5. Find the exact area of the surface generated by revolving the given curve about the y- axis, Draw…

A: Application of integration

Q: Find the area of the surface generated by e +e -y eY + e -y in the X= revolving the curve x= -In 3…

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Q: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

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A:

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: 8) Find the area of the surface generated by rotating about the x-axis the arc of the curve y x…

A:

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Q: Find the points on surface z^2=xy+4 closest to origin.

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Q: 6. Find the area of the surface formed by revolving about the curve defined by y = x2 - x2, 1<x<3…

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

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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: 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: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

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Q: ху — 4, 1 <x< 8

A: Surface area.

Q: Find the area of the surface generated when the given curve is revolved about the given axis. 5 ,…

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Q: Y=Ğ jfor exS3; about The X-axi's

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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…

A: