Find the flux of F(x, y, z) = x sqrt(x^2 + y^2) i + y sqrt(x^2 + y^2) j + z k through the portion of the cone z = sqrt(x^2 + y^2) that is on or below the plane z = 4 with upward orientation.

Q: Find the volume of the solid bounded by the surfaces x2 +y² = 2y, z = Vr2 + y² and the plane z = 0.

A: Given that : x2+y2=2yz=x2+y2  ,  z=0

Q: Find the moment of inertia about the z-axis of a thin shell of constant density δ cut from the cone…

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Q: Find the plane x/a + y/b + z/c = 1 that pass-es through the point (2, 1, 2) and cuts off the least…

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Q: Find the volume of the solid bounded by the surface z = f(x,y) and the xy-plane. Z= 30 - -R+y? v2

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Q: Find the centroid of the solid revolving the area bounded by y=x2 and x=2, and the x-axis about the…

A: Given, Three curves  y=x2 , x=2 and x-axis

Q: Find the volumes of the solids generated by revolving the regionsbounded by the lines and curves…

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Q: Determine the centroid of the lamina bounded by y=sin x, y= cos x and x= 0 in the interval 0,

A: Plot the curve and find the area of the area enclosed by the curves. The shaded region is the area…

Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

Q: The four corners of a thin homogeneous and square plate with side 2a are folded up so that they…

A: It is given that the side length is 2a.Let the total mass of the system is M.

Q: find the center of mass of the lamina bounded by the line y = %3D Ex+1 and the x and y axes|

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Q: Find the moment of inertia about the x-axis of a thin plate of constant density δ covering the…

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Q: Determine the centroid of the solid generated by revolving the area bounded by the curve y = x2, y=…

A: Given: The following figure is drawn for the given curve and a line.

Q: Determine the centroid formed by revolving about the y-axis, the a bounded by the curve y = x*, the…

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Q: Find the volume of the solid generated by revolving the triangularregion bounded by the lines y =…

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Q: Determine the location of the centroid of the solid formed by revolving about the y- axis, the area…

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Q: Find the mass of the solid bounded by the ay-plane, yz-plane, xz-plane, and the plane (x/3) + (y/2)…

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Q: how by integration that the centroid of a uniform semi-circular lamina of radius a from ne centre is…

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Q: A solid “trough” of constant density is bounded below by the surface z = 4y2, above by the plane z =…

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Q: Find the volume of solid generated by revolving the traingular region bounded by the curve y=4/x^3…

A: Given that y=4x3 and lines x=1 and y=12. The objective is to find the volume of the solid about y…

Q: Determine the centroid of the lamina bounded by y=sinx, y=cosx and x=0 in the interval 0,

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Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+6y+6z=24.…

A: Let's find.

Q: Calculate the moments of inertia of the triangle bounded by the straight lines x+y=1, x=0, y=0…

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Q: Find the volume of the solid bounded by the plane z = 10 - 5x - 8y and the coordinate planes in the…

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Q: Find the centroid (x¯,y¯)(x¯,y¯) of the region bounded by: y=7x^2+2x,   y=0,   x=0,   and   x=9?

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Q: Find the centroid of the homogeneous lamina bounded by the graph whose borders are f(x) = 16 − x2…

A: Let k be the density of the lamina body which is bounded by f(x) and (x-axis)

Q: Find the volumes of the solids obtained by rotating theregion bounded by the curves  y= x and  y =…

A: Note: As you are not mentioning about which axis, so we are solving about x-axis. For another axis…

Q: Find volume of the solid bounded by z = 0, f(x,y) = x² +y², x² + y2 = 62, 3y = -8x and 17y = 10x…

A: We will find out the required volume.

Q: . Find the centroid of the solid generated by the area bounded by y = sin x and the lines x = 0; x =…

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Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+5y+6z=33.…

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Q: Find the volume of the solid bounded from up by surface f (x,y) = 2x + y2 and from below by the…

A: According to question, surface :f(x, y) = 2x+ y2,Traingle vertices : 0, 2, 0, 0 and 3, 2

Q: Find the Surface Area of the solid generated by revolting the solid bounded by y=2√x, y=0, x=3,…

A: The Surface Area of the solid generated is given by,

Q: Find the centroid of a lamina enclosed between the circles of radius 1 and 2 centred at the origin,…

A: Consider the diagram of the lamina as per given information, The centriod of the lamina is defined…

Q: Find the volume of the solid of revolution bounded by the cirde x+y = 16, and the lines z = 0 and 8,…

A: Given curve is x2+y2=16 and line x=0 and x=8 about x-axis We have to find the volume of the solid of…

Q: Find volume of the solid bounded by z = 0, f(x,y) = x2 +y2, x2 + y2 = 52, 3y = -2x and 20y = 8x…

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Q: 4) Write the integral to calculate the outward flux through F = (-yx2, xy,-z) across the sphere with…

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Q: Find the moment of inertia about the x-axis of a thin plate of constant density d covering the…

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Q: What is the volume of the body of rotation formed by rotating the region bounded by the function y =…

A: Let us consider the given curve y=f(x) The volume of the solid of revolution about x-axis is…

Q: Find the volume of the solid bounded above by f(x,y) = 7x2, below by the xy-plane and the sides by y…

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Q: Find the centroid of the solid of revolution obtained by rotating the region bounded by y=x^3, y=8,…

A: We have to find the centroid of solid.

Q: Give an arclength parametrization of the line which is the intersection of the tangent planes of…

A: Let First, find the tangent planes at (1, -1, 0), (1, 2, 9).     Tangent plane at (1, -1, 0):…

Q: Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2 and the plane x…

A: Given Data The equation of the cylinder is z=12-3y². The equation of the plane is x+y=2.   Let, The…

Q: Find the center of mass of a thin plate of constant density & covering the given Region enclosed by…

A: Curve 1: y=x-x2 Curve 2: y=-x We have to find the center of mass.

Q: Find the volume of the solid bounded by the plane 8x + 5y + 10z = 7 in the first octant. Leave your…

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Q: The solid bounded by the surface y = x and the planes y +z = 4 and z = 0. %3D

A: You need to establish the limits for the integral and calculate that.

Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,2x]. y = sinx 1 3 4 5 1 1 2…

A: Let's find.

Q: Find the volume of the solid that lies under the plane 4x + 6y - 2z + 19 = 0 and above the rectangle…

A: To find volume set up triple integral ∬∫

Q: (2) Let S be the surface of the sphere of radius 4 centered at the origin oriented away from the…

A: We can apply divergence theorem to find this

Q: Find the volume of the solid bounded by the plane 7x + 3y + 4z = 3 in the first octant. Leave your…

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Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density δ =…

A: Given: y=2x and y=4 Thus the region bounded by the y-axis and the line y=2x and y=4 is shown as…

Q: Determine the centroid of the solid generated by revolving the area bounded by the curve y = x²,y =…

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