Let G be the solid enclosed by the plane z= y, the xy-plane, and the parabolic cylinder y = 1-x2. If ch(x) rg(x.y) y dzdydx, 0. G then g(a,2b)+h(2b)=

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

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Q: Let F(x, y, z) = z tan-(y²)i + z³ In(x² + 2)j + zk. Find the flux of F across S, the part of the…

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Q: z dv, where E is enclosed by the paraboloid z = x2 + y² and the plane z = 4. Evaluate

A: see 2nd step

Q: Consider I=E∫x3dx1dx2dx3, where E: x12 + x22 ≤ x23, 0 ≤ x3 ≤ 1,that is, E is the solid bounded by…

A: a)  The surface has a solid region, E={(x1, x2, x3): -1≤x1≤1, -1≤x2≤1 and 0≤x3≤1}, which is a cone…

Q: Let F(x,y,z) = ztan(y2) i + z³In(x² + 4)j+z k. Find the flux of F across the part of the paraboloid…

A: Given that, F(x,y,z)=ztan-1(y2)i+z3ln(x2+4)+zk To find flux of F: Divergence theorem:…

Q: The region W lies between the spheres x2+y2+z2=1 and x2+y2+z2=9 and within the cone z=x2+y2−−−−−−√…

A: Given: The region W lies between the spheres       x2 + y2 + z2 = 1 and x2 + y2 + z2 =9 with in the…

Q: . Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = y², xy-plane and…

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Q: Use Stokes theorem to evaulate ⌠c F*dr where F(x,y,z)=2i+yj-xk and C is the boundary of the part of…

A: F(x,y,z)=2i+yj-xk C: z=9-x^2-y^2  z=0

Q: The surface area of the part of z = 2 + V4 – x² – y² that lies inside the paraboloid z x² + y² is

A: This is a problem of vector calculus.

Q: a) Let G be the wedge in the first octant that is cut from the cylindrical solid y² + z? < 4 by the…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y°, the cylinder z² + y² = 2, and…

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

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Q: Let G be the solid enclosed by the plane z= y, the xy-plane, and the parabolic cylinder y = 1-x². If…

A: Consider the given information,

Q: F = (x² – y²,x, 2yz); C is the boundary of the plane z = 6 – 2x – y in the first octant.

A: Given, F=x2-y2,x,2yz Find the line integral ∮CF·dr in the following. Here C is the boundary of the…

Q: Evaluate /// 203 dV G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Here we have to find range of values for x,y and z and then find triple integral

Q: a) Let G be the wedge in the first octant that is cut from the cylindrical solid y² + z² ≤ 4 by the…

A: To Evaluate: ∫∫∫GxyzdV. Where G: y2+z2≤4, y=2x , x=0. As per policy, we are solving only thr first…

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: If S is the solid bounded by the paraboloid z = 3x2 + 3y and the plane z = 4 (with constant…

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Q: Use Stokes's theorem to evaluate OF.dr for the given F and C. (c) F(x, y, z) = xzi+ xyj– 3xz k, C :…

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Q: Evaluate where G is the solid in the first octant bounded by paraboloid : = + y, the cylinder r+ y 9…

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Q: • SSS ²³² x² + y² = 2, and the xy plane. Evaluate e² dV where E is enclosed by the paraboloid z = 6…

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Q: Let G be the solid enclosed by the plane z = y, the xy-plane, and the parabolic cylinder y = 1-x²…

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Q: Let F(x, y, z) = z tan-¹(y²)i + z³ In(x² + 3)j + zk. Find the flux of F across S, the part of the…

A: The given problem is to find the flux of vector field over the given surface of part of the…

Q: 2. A solid G is bounded by the paraboloid z = 4-²-y², the cylinder x² + y² = 4 and the plane z = 5.…

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Q: Let G be the solid enclosed by the plane z = y, the xy-plane, and the parabolic cylinder y = 1-x²…

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Q: Evaluate the triple Integral. 3xyz dV, where T

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Q: Consider D to be the region below the paraboloid z = 3+x² + y² , inside the cylinder x + y² =1 and…

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Q: 3. Evaluate /// 2* dV if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: triple integral

Q: CALCULATE S SS F(x, y, z)dxdydz WHERE: T f(x, y, z) = x AND "T" IS THE SOLID DELIMITED BY THE…

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Q: Consider the solid Q that is generated in the first octant by the surfaces S, : 2x + 3y + 3z = 6 S,:…

A: The region S2 is clearly a parabola y2 = 2-x and it is symmetrical in the x-axis.

Q: 1) Consider the solid Q in the first octant, generat surfaces: z = (y – 3)² + 1, 2r + 4z = 16, 1= 1,…

A: Volume of solid: Let z=f(x, y) and z=g(x, y) be the functions of x and y of a solid, and let x=a to…

Q: Evaluate || F-n dS where S is the cylinder (including the disk on the bottom) x² + y² =1 for 0<z<1…

A: First, we plot the given surfaces.Cylinder : x2+y2=1; 0≤z≤1Paraboloid : 3x2+3y2+z = 4; 1≤z≤4.

Q: Let F(x, y, z) = z tan-1(y2)i + z3 In(x2 + 4)j + zk. Find the flux of F across S, the part of the…

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Q: 3. Evaluate AP G if G is a solid in the first octant bounded by the plane y + z = 2 and the surface…

A: The given problem is to evalute the triple integral over the given surface of first octant bounded…

Q: Let  F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 10)j + zk.  Find the flux of F across S, the part of…

A: let, F(x,y,z)=ztan−1(y2)i+z3ln(x2+10)j+zk Find the flux of F across the part of the…

Q: Use Gauss’ theorem to evaluate F.ndS for the given F and o. (b) F(x, y, z) = x³ i+x?yj+xy k, o : the…

A: We will use gauss divergence theorem to find value of given surface integral  If E is a  simple…

Q: Evaluate G if G is a solid in the first octant bounded by the plane y +z = 2 and the surface y = 1–…

A: Use the following formulae, to obtain the solution. a-b2=a2-2ab+b2∫xndx=xn+1n+1+C

Q: É = ( 2x3 + y°, y3 + z³, 3y²z), S is the surface of the solid bounded by the paraboloid z = 1– x2 –…

A: We will find out the required flux.

Q: Let F(x, y, z) = z tan-(y2)i + z3 In(x2 + 1)j + zk. Find the flux of F across S, the part of the…

A: Divergence Theorem states that  Where S is a closed surface, and E is the region inside that…

Q: Evaluate € fff.₂²². e² dV where E is enclosed by the paraboloid z = 3 + z² + y², the cylinder z² +…

A: We need to find integral.

Q: Let G be the solid enclosed by the plane z = y, the xy-plane, and the parabolic cylinder y = 1-x²…

A: Given: G be the solid enclosed by the plane z = y, the xy – plane and the parabolic cylinder y =…

Q: (a) Given F(x, y, z) = –xi– y j+x²k and o is the surface of the solid bounded by the Vx² + y² and…

A: There is no specific introduction for this question. Please go through the solution.

Q: 7. Find the flux of F(z,y, 2) = ri+yj+zk through the portion of the paraboloid z = 1+z²+y° that is…

A: Given

Q: where F(x, y, z) = (ry, x²y, y) Use Gauss's theorem to calculate where is the paraboloid z = 4 – x²…

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Q: Let F(x, y, z) = z tan-(y2)i + z³ In(x2 + 9)j + zk. Find the flux of F across S, the part of the…

A: Get points of intersection of the paraboloid and z=3:  Thus, point of intersection is a circle in…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x + y°, the cylinder + y = 1, and the ry…

A: To Determine: evaluate ∫∫∫eZdV  where E is enclosed by the paraboloid z=5+x2+y2,the cylinder…

Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

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Q: 2. Evaluate the triple integral / || y dV; G is the solid enclosed by the plane z = y, the xy-plane,…

A: Solution is given below;

Q: 1.Find the area of the surface. a. The part of the plane 2x + 5y + z = 10 that lies inside the…

A: Note : As per our guidelines we can supported to answer only first three subparts