Use line intaral to find the aren af the surface het extends upward from the Part of the ellipse *= 13 Cest,y = 12 Sint, o atsĘ in the sxy-plane to the surface. Z=xy.

Q: * :classify the surface. 1 – y = 5x² + 6z? Cone O Plane O Ellipsoid O

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Q: find a parametrization of the surface. 1.The surface cut from the parabolic cylinder y = x2 by the…

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Q: Find the area of the surface generated by generated by revolving the curve about the r-axis. と4u:4+…

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Q: The plane y=2 intersects the elliptic paraboloid ē =4x ty parabobo. Fied the slope ot the fangenh to…

A: Given :     y = 2      z = 4x2 + y2

Q: The area of the surface obtained by rotating the curve y = 22 x + 1, 0 < x < 44 about the x-axis is

A: Consider the given curve. y=22x+1 in the interval 0≤x≤44 The problem requires to find the area of…

Q: Find the surface area of the surface resulting from revolving the curve -= 2x+1 on the interval…

A: Putting the formula of surface area we have

Q: find a parametrization of the surface. The cap cut from the sphere x2 + y2 + z2 = 9 by the cone z =…

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Q: Find the area of the surface generated by revolving x = t+2/3, y = +2/3t+3, -2/3 sts2/3 about the…

A: The surface area of disk is s=πr2 h  where r is radius and h is width

Q: a. Find the area of the surface generated by revolving about the x-axis the loop of the

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Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x, 0 <xs;…

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Q: Consider the ellipsoid 4x? + y?+ 222 = 25. Find all the points where the tangent plane to this…

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Q: Find the area of surface that is generated by revolving the portion of the curve 9 – y² , – 2 < y< 2…

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Q: Find the area of the surface generated by revolving the curve y = Vx + 3, 4 < y <7 around the…

A: We have to find area of the surface . Given y=x3+3                                 4≤y≤7

Q: Find the area of the surface cut from the paraboloid x² + y² -z = 0 by the plane z = 6. The surface…

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Q: Find the area of the surface obtained by rotating the curve x = /16 – y², 0 <y<2, about the y- axis.…

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Q: Find the area of the surface generated by revolving x =t+ 2/5, y= +2/5t, -2/5 sts2/5 about the…

A: Here we will find out area of surface of revolution.

Q: find a parametrization of the surface Circular cylinder band The portion of the cylinder (x - 2)2…

A: Given: The portion of the cylinder (x - 2)2 +z2 = 4 between the planes y = 0 and y = 3 To find:  a…

Q: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1/3 ( y2…

A: Given curve is x=13y2+232 over 1 ≤ y ≤ 2. The exact area of the surface obtained by rotating the…

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 8t,    y =…

A: Given, x=8t, y=7t, 0≤t≤5

Q: Asap Find the characteristic strips of the equation ap+yq-pq = 0 and obtain the equation of the…

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Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: Find the area of the surface obtained by rotating the curve x = et - t, y = 4e/2, 0<t<1 about the…

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Q: Find the area of the surface. The part of the surface y = 4x + z2 that lies between the planes x =…

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Q: Classify the surface: 1- x = 3y? + 4z2 O Plane O sphere O cone O Elliptic paraboloid O Ellipsoid

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Q: Find the area of the surface generated by revolving the curve                             x = 4t, y…

A: If x = f(t), y = g(t) then surface area is 1) About x axis: A=2π∫abydxdt2+dydt2dt 2) About y axis:…

Q: Find the area of the surface. The surface in the first octant cut from the cylinder y = (2/3)z^(3/2)…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3(y2 +…

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Q: Find the area of the surface generated by revolving x = t+2/3, y =+2/3t+1, -2/3 sts2/3 about the…

A: Find the area of the surface generated by revolving the graph of the following parametric equation…

Q: Determine the projection of the surface - y = z on the xy-plane? (Hint: z = 0) O Hyperbola O Ellipse…

A: projection of the surface

Q: Find the area of the surface. The portion of the plane y + z = 4 that lies above the region cut from…

A: Given:

Q: Determine the projection of the surface – y : = z on the xy-plane? (Hint: z = 0) Ellipse O Hyperbola…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3(y2 +…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 8t, y = 7t,…

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Q: Example Find the exact area of the surface obtained by rotating the curve y? = x + 1, 0 <x< 3, about…

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Q: 3- Find the surface area of the solid obtained by rotating the curve z= 2/4- y; 0Sysabout the…

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Q: Classify the surface: 22 = 3y? + 22 %3D O Ellipsoid O cone O sphere O Elliptic paraboloid O Plane

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Q: * = -. y = 4 y = 4, 0 < t < 1 0 <t < 1

A: Given curve is x=4t−43t3 and y=4t2, 0≤t≤1. We have to find the area of the surface obtained by…

Q: Find the area of the surface generated by revolving the curve about each given axis. X = 4t, y = 8t,…

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Q: Find the points on the surfacex – yz = 36 that are closest to the origin. Enter your answers in…

A: Given : x² - yz = 36

Q: Find the area of surface that is generated by revolving the portion of the curve x = V64 – y² , – 2…

A: Solution :-

Q: Find the area of the surface obtained by rotating the curve y=1/33/2, 0 ≤ y≤12  about the y - axis.

A: To find the area of the surface obtained by rotating the curve

Q: The area of the surface obtained by rotating the curve y = V9-x2, -3 < x < 3 about the x-axis is

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Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: • Find the area of the surface generated by revolving about the x-axis the upper half of the ellipse…

A: IN THIS QUESTION WE HAVE TO FIND AREA FROM REVOLUTION OF A ELLIPSE.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  x=1/3(y2 + 2)…

A: The given curve is,

Q: Find the surface area of the surface generated by revolving a portion of the curve y = x", from x =…

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Q: Find the area of the surface obtained by rotating the curve y2 = 4x + 4 0<x<8 about the x-axis? %3D

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Q: ii) Find the exact area of the surface obtained by rotating the curve 1 12x 3 y = x³ + 9 1 ≤ x ≤ 2,

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. (y2 + 2)3/2, 2 <…

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