Use a parametrization to express the area of the surface as a double integral. Then evaluate the integral. 1 x + y +z = 4 by the cone z = V3 The lower portion cut from the sphere :

Q: Use a line integral to find the area of the surface that extends upward from the parabola y = x (0…

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Q: Evaluate the triple integral R. where R is the region enclosed by the sphere r2 + y² + 2? = 9.

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Use a triple integral to find the volume of the solid below the paraboloid z = x2 + y2 and above the…

A: The given problem is to find the volume of solid bounded below by paraboloid and bounded above by…

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

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Q: Find the surface area generated by revolving the curve C : x(t) = 3t, (0 < t < 1) y(t) = 2t about…

A: Use the formula for the surface Area when a parametric curve rotated about y-axis.

Q: Use a spherical coordinate integral to find the volume of the given solid. the solid bounded below…

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: We need to find volume.

Q: Set up the following triple integral, but do not calculate it: a solid above the xy-plane, inside…

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Q: Find the surface area of the portion of the cone z=ax +y within the cylinder x+y =1.

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

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Q: Use the shell method to write and evaluate the integral that gives the volume of the solid generated…

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Q: Find the volume of the solid of revolution generated when the area described is rotated about the…

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Q: Use a triple integral to find the volume of the solid enclosed by the paraboloid x=3y^2+3z^2and the…

A: First compute the limit as follows.

Q: Use the shell method to write and evaluate the integral that gives the volumme of the solid…

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Q: f(x) = and the x-axis on the interval [2, 0) 7e*

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Q: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x² + z2 and y…

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Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x + y2 =…

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Q: Find the surface area of the surface given by the portion of the paraboloid z= x² + y´ that lies…

A: The surface area f(x,y) above the region R of the XY plane is given by  ∫∫R(fx)2+(fy)2+1dxdy , where…

Q: Find the volume of the region bounded above by the sphere r = 2a cos0, and below by the cone = a…

A: Given: the sphere r=2a cos theta , cone ϕ=α0&lt;α&lt;π2

Q: Use the shell method to write and evaluate the integral that glves the volume of the solid generated…

A: We will find the volume of the solid region as following.

Q: (c) By using double integrals, find the surface area of plane 2x + 5y + z = 10 that lies inside the…

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Q: (b) By using double integrals, find the surface area of the portion of hemisphere z = /25 – x2 – y²…

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Q: Find the surface area of the planez= x +y?from z=4 to z=9?

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Q: f (x, уy) %3D — 3х — 2у + 6 | R = {(x,y) : 0 <x< 2,0< y< 2 – x )}

A: Given query is to find the area bounded by the region.

Q: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x2 + z? and y…

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Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

A: Given- Cone: z=3x2+3y2 Sphere: x2+y2+z2=z To set up the triple integral that will give the volume of…

Q: Find the surface area generated by rotating the portion of the curve x-y = 0 from x 0 to x = 2 about…

A: We have to find surface area

Q: set up, do not evaluate, the double integral for the surface area of the portion of the paraboloid…

A: The solution are next step

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: To find the volume

Q: Find the surface area of the cone z = ' + y² that lies between the plane y = x and the cylinder y =…

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Q: Evaluate the integral p(x? – 2y?) dA ,where R is the fir - quadrant region between the circles of…

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Q: Use a triple integral to find the volume of the solid enclosed between the elliptic cylinder a² +…

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Q: Use a line integral to find the area of the surface that extends upward from the parabola y = x² (0…

A: We have to use a line integral to find the area of the surface that extends upward from the parabola…

Q: Find the area of the part of the surface z = xy that lies within the cylinder x2 + y2 = 9.

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Q: x? = 4 - z S z= 3x Y

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: Integration within specific limits of the variable is known as definite integration. The integration…

Q: Use a Spherical Coordinate integral to find the volume of the solid bounded above by the sphere p =…

A: Given, Region is bounded above by the sphere and below by the cone .

Q: Evaluate the triple integral AP 2 over the solid region E enclosed by the two surfaces z= 4/z² + y?…

A: The given solid is bounded by the surfaces z=4x2+y2 and z=x2+y2. Find out the intersection of the…

Q: Evaluate the triple integral /| z dV where E is the solid region enclosed by the paraboloid z = x? +…

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: The given plane is 7x+y+z=4The given region is tetrahedron enclosed by by coordinate…

Q: Use spherical coordinates to calculate the integral SSgr+y°dV over the region E which is the portion…

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Q: HW: Find the area of the surface generaled by revolving 1. LIIC 2. y = Vx- xã , 1 sxs3 about x2, 1…

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: To find the volume using a triple integral, we need to determine the bounds of integration…

Q: Set up, but do not evaluate, an integral that's equal to the surface area of the surface formed by…

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Q: Use a line integral to find the area of the surface that extends upward from the parabola y =x…

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: This question is related to definite integral, We will solve it using given information.

Q: HW: Find the area of the surface generaled by revolving x = /y, 1 <y <8 about the X axis. 1. 3 2. y…

A: we have to find the area of the surface generated by the revolving the curves about x axis. since…

Q: Set up but do not evaluate the integral used to find the area of the surface generated by revolving…

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