6. Consider the solid Q bounded by the surfaces S1 : 1 = 4 – 22 S2 : 1+y = 5 S3 : 1 = 0 S4 : y = 0 Sz : z = 0 That is shown in the figure:

Q: 7) z dV, E is the solid enclosed by the cylinder r2 +y = 1, and the E planes z = 0 and z 3.

A:

Q: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: 1. A solid G is bounded by the paraboloid z = 4 – x² – y², the cylinder x² + y? = 4 and the plane z…

A:

Q: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: 5. . Find sSSzdv where D is the 2 solid bounded by xty'tz=4 and 2= 13x²+ 3y2. (" sce Cueam Come')

A:

Q: 2) Evaluate the following line integral: . 0+z)dx + (x + z)dy + (x + y)dz where C consists of the…

A: C1: (0,0,0) to (1, 0, 1)x-01-0=y-00-0=z-01-0=tx=t, y=0, z=tdx=dt, dy=0, dz=dtI1=∫01[(0+t)+(t+0)]…

Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A: Parametrize the three curves separately and c is the sum of the three integrals.

Q: If f (0)=f'(2), find the difference c-2d for the following cubic spline S(x) with clamped boundary…

A:

Q: 3. Set up the integral to find fSfr r dV where T is the tetrahedron in the first octant under the…

A:

Q: 1. Evaluate the integral: I = 2x drdydz where the solid S is defined as: S = {(r, y, z) E R³:x > 0;…

A:

Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A: We need to find the length of the curve BD. The curve BD is found by the intersection of the…

Q: Without using the formula (Gauss), calculate S=∂E∫F(x).n(x)ds, where F(x) = x32k ,E : x12 + x22≤ x3,…

A: Typing the equation may be some mistake. 0≤x3≤1 and another 0≤x3≤11, first one i accept.

Q: The solid bounded by x = y? – 1, z = 1 – y², z = 4 – x, and z = 0.

A: Given that,

Q: 3. Evaluate , (x + z)dS where the surface S is the first-octant portion of the cylinder y² + z² = 9…

A: Step:- 1 Since, we know Surface integrals ∫∫Sf(x,y,z)dS=∫∫Df(x,θ) rx×rθ dxdθ…

Q: Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If F = 2y i - zj + x²k and S is the surface of the parabolic cylinder y²= &x in the first octant…

A:

Q: Q1 (9 M)/ Use Gauss's theorem to evaluate ff. F.ds where F= 4xi - 2y'j +z°k and S is the surface…

A: We have to evaluate the integral ∬SF·ds where F=4xi-2y2j+z2k and S is the surface bounding the…

Q: 5. If F=2xi - xj + y*k, evaluate ffLF av over the region bounded by the surfaces x = 0, y = 0, y = 6…

A: Given: F→=2xzi∧-xj∧+y2k∧region bounded by the surface x=0,y=0,y=6 and z=x2 ,z=4

Q: Considering f(x, y, z) = z + x²y and S as part of the cylinder y? + z² = 25 that is between the…

A: Given that, fx,y,z=z+x2y and S is the part of the cylinder y2+z2=25 that is between the planes x=0…

Q: | eョで)) dV=

A: Given:              ∭Dex2+y2+z232dv        d is the region in the first octant between spheres…

Q: Set up the integral [ s (x, y,z)dV six different ways where E is the solid in the first octant…

A:

Q: 18. Evaluate § (9 − x² − y²) dV, where H is the solid hemi- sphere x² + y² + z² ≤ 9, z ≥ 0.

A:

Q: 3. Calculate the circulation of A=p coso ap+ z sino a: around the edge L of the wedge defined by 0≤p…

A: Here we have given that, A=ρcosϕaρ+zsinϕaz and wedge is defined as, 0≤ρ≤2, 0°⩽ϕ≤60° and z=0 as shown…

Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: Consider the solid Q that is generated in the first octant by the surfaces S1 : y+z = 4, S2 : y - 1…

A: Solution is below.

Q: T// Vx² + y² dV, where E is the solid in R3 bounded by the surfaces E z = x² + y² and z = 8 – x² –…

A:

Q: Find the difference c-d for the following cubic spline S(x) with natural boundary conditions: S(2) =…

A: To find - Find the difference c - d for the following cubic spline S(x) with natural boundary…

Q: 6. Set up the integral /| f(x, y, 2) dV E where E is the solid that lies under x + 4y + 6z = 12 in…

A:

Q: 2) Evaluate the following line integral:S. (v + z)dx + (x + z)dy + (x + y)dz where C consists of the…

A:

Q: Which of the additional conditions below can be used to obtain a clamped cubic spline S(x) passing…

A:

Q: 2. Set up the triple integral f[Sp I+y+zdV, where D is the tetrahedron with vertices at (0,0,0),…

A:

Q: One of the following regions guarantees the uniqueness theorem of first order LV.P. 2x-y y(0)=23. dx…

A:

Q: 3.33 Let D = 2pz'a, + p cos´ þa,. Evaluate (a) $D· dS (b) J,V· Ddv over the region defined by 2 < p<…

A: Given: Let D=2ρz2aρ+ρcos2ϕaz a∮SD.dS Here, We know that surface vector dS is defined as…

Q: So lve the se cond order boundary Valye eF problem: Y+y+2yso where y (0) = || and y'lo)s 18

A: The given differential equation is y''+y'+2y=0......(1) with boundary conditions y0=11 and y'0=18…

Q: Sketch the solid described by the given inequalities. 0srs 8, -T/2 se S T/2, 0szs 1. 1.0 1.0 z05…

A:

Q: (c) Find II zdV where E is the region bounded by the cylinder y² + z² = 9 and the planes E x = 0, y…

A:

Q: A solid G is bounded by the paraboloid z = 4 – x2 – y?, the cylinder x2 + y? = 4 and the plane z =…

A:

Q: 9. The solid bounded by x = 1 – y?, z = y², x = 5, and z = 9.

A:

Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A:

Q: 5. Evaluate z dV, where E is bounded by the cylinder y? + z2 = 9 and the planes x = 0, y = 3x, and z…

A:

Q: 6. Consider the solid Q bounded by the surfaces Sį : z = 4 – 22 S2 : 1+ y = 5 S3 : 1 = 0 Sa : y = 0…

A: Given : solid Q bounded by the surfaces      S1 :x=4-z2S2 :x+y=5S3 :x=0S4 :y=0S5 :z=0 When…

Q: 1) Evaluate the triple integral SS, f(x,y,z)dv : B) f(x,y,z) = 3y² – 2z , Q is the tetrahedron…

A: given f(x,y,z) = 3y2-2z, Q=3x+2y-z=6 The region bounded by the equation Q is a tetrahedron cutting…

Q: 6. Evaluate the integral fSSp 4y dV if D is bounded by the elliptic paraboloid z = 3.x?+y²+1 and by…

A: Application of integration

Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A: In this question, we use the given sketch of the surface and find the parametrization for each…

Q: Evaluate || 4.nds , where A=zi+xj – 3y°zk and S is the surface of the cylinder x² + y =4 included in…

A: Let ∅=x2+y2-4  Then the normal to the surface S is ∇∅=2xi+2yj The unit normal is…

Q: The solid bounded by the surfaces S : -2(: – 2) = y² S2 : 1 = 5– 2y S3: r=0 S4 : y = 0 Ss : z = 0…

A:

Q: 4. Evaluate x²dV G where G is a solid that lies in the first octant bounded by x? + y? = 3z and z =…

A:

Q: Consider the solid Q shown in the following figure 2.x + 3y + 3z = 6 S y? + x = 2 2 If S: 2x + 3y +…

A: The given surface is as follows: 2x+3y+3z=63z=6-2x-3yz=136-2x-3yz=2-23x-y The projection of the…

Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A:

Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

A: