Q17// If F = i+ yj + k , Evaluate S, F dv where Vis region bounded by the plane z=0 and the surface x? + y?+ z² = 4 forz 2 0

Q: find the volume of the solid bounded by y=2x+1,y=3and x=4 about using the line y=10 the cylindrical…

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Q: Find volume of the solid bounded by z = 0, f(x,y) = x² + y², x² + y² = 4², 10y = -6x and 13y = 8x…

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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 volume of the solid bounded by the surfaces f(x,y) = 4x2 + 4y2, z = 0 and 6x2 +6y2 = 9.…

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Q: 3.find the volume of the region bounded by the surface y=x^2,y+4x+5 and the plane z=0 and z=4

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Q: 4) Find the volume bounded by the plane z = 0 laterally by the elliptic cylinder x'+4y 4 and above…

A: Triple integral is used to integrate function of three variable over three dimensional region. It is…

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: Let S be the part of the plane x + y + z = 2 in the first octant. If we change the surface integral…

A: Given: From the above expression, z=2-x-y Partially differentiate the above expression with respect…

Q: Q5) Find volume of body bounded by z = x – y from below and z = x +y from Above inside y = x² ,y =…

A: Volume bounded by the region

Q: Given a solid is bounded above by the surface z = 4x2 + 7y2 +1, xy-plane, x = y?, x = 4. If the…

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Q: Find the centroid of the solid formed by revolving about ox the area bounded by y? = 2x and the line…

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Q: Let F(x, y, z) = 2xi – 2yj + z²k. Evaluate Is where S is the cylinder x2 + y2 = 9 with z E [0, 1].…

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Q: 24. Dis bounded by the plane z = 2y and by y = 4- x. 6(x. y.z) = y'lb/in. (Note: this is the same…

A: The triple integration is given by: v=∫∫v∫dv

Q: Find the volume of the solid bounded above by the graph of f(x, y) = 2x + 4y³ and below by the…

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Q: Find the volume V under the the plane z = 8x + 6y over the region R = (x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤…

A: We have to find the volume under the plane z=8x+6y over the region R=x,y:0≤x≤1,0≤y≤2x2 (a) Draw the…

Q: Use spherical coordinates to evaluate the integral ʃW (1 / sqrt(x2 + y2 + z2)) dV where W is the…

A: We need to use spherical coordinates to evaluate the integral ʃW (1 / sqrt(x2 + y2 + z2)) dV where W…

Q: Evaluate the surface integral. xz dS S is the boundary of the region enclosed by the cylinder y2 +…

A: To evaluate the surface integral               ∬Sxz dS where S is the boundary of the region…

Q: A right circular cone is generated by revolving the region bounded by y = hx/r, y = h, and x = 0…

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Q: Let T be the region in the first octant bounded by the parabolic cylinder z = 25 – x? and the plane…

A: Consider the given information: Let T be the region in the first octant, bounded by parabolic center…

Q: É X pressthe inteoral SSS, fCxy, Z) dv as aniteratedintegral in six different ways, where Eisthe…

A: Given the solid E is bounded by the given surfaces z=0,x=0,y=2,z=y-2x. Find the six different…

Q: Find the areas of the regions 1. Bounded by the spiral r = 0 for 0 < 0 < T r = 0 2'2 х (п, т)

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Q: Find the volume of the solid bounded above by z = 1- (22 + y²), bounded below by the ay-plane and…

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Q: grad V dS where V = x + y² + z² and S is the surface x2 + y? = 4 bounded by z=0,z=4 ,x=0,y=0? Q11//…

A: Given that, V=x+y2+z2 and S be the surface x2+y2=4

Q: Evaluate the double integral // vdA R. where R is the region in ry plane bounded by y = |r| and y =…

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Q: Q2) Find the volume of the solid generated by revolving the "tri- angular" region bounded by the…

A: Washer method: To find the volume enclosed between two functions, the washer method is applied. We…

Q: Solve for the area of the portion of the cylinder x = V1 – y², which lies between the planes z = 0…

A: Line integral

Q: Q5) Find volume of body bounded by z = x-y from below and z = x + y from Above inside y = x2 y = 2.

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Q: Find volume of the solid bounded by z = 0, f(x,y) = x2 +y?, x2 + y2 = 3?, 6y = -7x and 15y = 4x…

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Q: Find the volume of the region D enclosed by the region cut from the cylinder x2 + y2 4 by the plane…

A: Find the limit of the x, y and z:

Q: Find the volume of the solid bounded by the surfaces z + y = 2y, :- V+ y and the plane z-0. 3.

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Q: z= f(x,y)=2x+y from the top with the plane R=((x,y) 3...  calculate the volume of a body bounded…

A: The volume under the surface over the region D can be calculated by the following formula.

Q: Find the volume of the solid bounded by the surfaces f(x,y) = 10x² + 10y², z = 0 and 4x2 +4y2 = 7.…

A: Given,  f(x,y)=10x^2+10y^2  ,  z=0  ,  and  4x^2+4y^2=7

Q: Find the polar moment of inertia of the region in the xy plane bounded by x² - y? 1,x2- y2=9, xy…

A: Solution is in step 2

Q: Find the volume of the solid in the first octant bounded above by the surface z = 3(4 – y²), and…

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Q: Use cylindrical coordinates to calculate SS lw f(x, y, z) dV for the given function and region: f(x,…

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Q: Find the volume of the solid bounded by the surfaces f(x,y) = 4x2 + 4y?, z = 0 and 2x2 +2y2 = 4.…

A: Here we can use polar coordinates to find the volume. Formula for volume using polar coordinates is…

Q: Compute the moment of inertia with respect to the 0z axis (i.e. the integral of the square of the…

A: We will sketch first. Then using Triple integration we will find the Moment of Inertia

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: What is the volume of the region coming from the cylinder {(x, y, z) : x^2 +y^2 ≤ 1} sliced by the…

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Q: Find the volume of the solid bounded by the surfaces f(x,y) = 6x2 + 6y2, z = 0 and 7x2 +7y2 = 3.…

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Q: Find the volunme of the solid generated by revolving the region bounded by y = 4x - 2* and y/ the…

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Q: Find the volume of the solid obtained when the region bounded by the lines y = 1, r = 1, 1 = 2 and…

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Q: Use cylindrical coordinates to evaluate f(x,y)= sqrt(x^2+y^2) in the region bounded by x^2+y^2 =1…

A: Let's find.

Q: Find the volume of the solid D bounded from above by the surface z = 9 − 4x2 − 4y2 and below by the…

A: Consider the given surface z = 9 − 4x2 − 4y2 and below by the plane z = 0. ⇒ 0 = 9 − 4x2 − 4y2  ⇒…

Q: Evaluate the integral. z dx dy da W is the region bounded by the planesx0, y 0,0, z-1, and the…

A: Evaluation of the triple integrals, uy conversion of cylindrical coordinates

Q: Let the spatial bady be the region between ま=8- x2+y the Cone and the plane まdV integral

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Q: Find volume of the solid bounded by z = 0, f(x,y) = x² +y², x² + y² = 4?, 4y = -5x and 13y = 6x…

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