1- Calculate the surface integral Sl,G(r)dA, where G = (1+%rz)ź and S is given by the parametrization r(u, v) = [u, v, 2u*], 0 < u < 2, 0

Q: Evaluate the double line integral S  of the fuinction (x − 2y + z) dS. S: z = 9 − x,  0 ≤ x ≤ 9,  0…

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Q: 3.4.8 Evaluate the area of the surface z = 2-x² - y² lying above the (x, y) plane. (Hint: Use polar…

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Q: Evaluate the triple integral. 2xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: Evaluate the triple integral |// xy dV where E is the solid tetrahedon with vertices (0,0,0), (7, 0,…

A: Consider the following: Equation of plane passing through 7,0,0,0,5,0,0,0,10x7+y5+z10=1x ​ranges…

Q: 6. Compute the area of the surface for 0 <u 1, 0 < v < using the first fundamental form..

A: Given xu,v=u2-cosv,u+sint,cosv

Q: .Find the exact value of the double integral. J (2x + 5y) dA, where R is the rectangular region…

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Q: 5. Let S be the negatively oriented surface defined by R(u, v) = (u², v², uv), where (u, v) = [0, 1]…

A: Given That : R(u,v) →=u2,v2,uvF(x.y,z)→=z,z,xy Find : Double integral which is equal to the flux of…

Q: Evaluate the line integral (x+2y)dx + dy, where C consists of the path C from (0,0) to (3,0), the…

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Q: Use Green's Theorem to evaluate the line integral. (a) | e2a+y dx +e¬Y dy, where C'is the triangle…

A: In the question we have to evaluate integral. NOTE - As per Bartleby's policy we can not solve…

Q: Evaluate the triple integral ∫∫∫T (x^2) dV where T is the tetrahedron with vertices (0, 0, 0), (1,…

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Q: A flux is given by F = x²y³ i – xy j. Verify the Green's theorem for the region bounded by the…

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Q: Evaluate the triple integral. I/| (x - y) dv, where E is enclosed by the surfaces z = x2 - 1, z = 1…

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Q: a)Calculate the integral [D zdV on the D region bounded by the 6 = x2 + y2 paraboloid from the…

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Q: 7. Use Stokes's Theorem to write S.(2y² + 6x*)dx + (2x² + 7y³)dy+ (2z° – yz)dz as a surface integral…

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Q: Evaluate the triple integral I/| (x, y, z) dV over the solid E. f(x, y, z) = vx2 + y², E = {(x, y,…

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Q: Use Green's Theorem to evaluate the line integral: f. In(1 + y) dr – #, dy where C is triangle with…

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Q: Given a solid is bounded by f(x,y) = 8x² + 8y², x² +y² = 3?, 3y = 4x and x = 0 in the first octant.…

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Q: Evaluate the triple integral. 16.  ∫∫∫T  xz dV , where T is the solid tetrahedron with vertices…

A: The solid tetrahedron T with vertices 0, 0, 0, (1, 0, 1), (0, 1 ,1) and 0,0, 1. The solid region is…

Q: 1) Evaluate the integral SRW (x,y,z)dV with W= e*-y-z where R is a rectangular box with corners at…

A: As per Bartlebys answering policy, we can answer only one question, so kindly post the remaining…

Q: 6- Evaluate the line integral ScF · dr, where F = [xy, yz, xz] and C is the boundary of the…

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Q: Evaluate the following line integral by two methods: (a) directly; (b) using Green's Theorem. $y²dx…

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Q: 5. Let S be the negatively oriented surface defined by R(u, v) = (u², v², uv), where (u, v) [0, 1] x…

A: This is the problem from Vector Calculus.

Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

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Q: Suppose f(x, y, z) = x² + y² + z? and W is the solid cylinder with height 9 and base radius 5 that…

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Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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Q: Evaluate the triple integral ∭E(x+2y)dV where E is bounded by the parabolic cylinder y=2x2 and the…

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Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: 9. Evaluate the line integral of F = (2xy + 1,x² + 2yz, y? – 2) over the region C parametrized by…

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Q: 3. Calculate the volume of the closed body formed with the surfaces; "y?+ (z-1)? = 1, x=2 and x+z=5"…

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Q: Use Green's Theorem to evaluate the line integral. y dx + 7x dy C: square with vertices (0, 0), (0,…

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Q: Evaluate the triple integral. SSLĘ 8x dV x = 2y2 + 2z2 and the plane x = 2. where E is bounded by…

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Q: Set up an iterated double integral for the flux integral S ſ, F•dS where F(x, y, z) = ri+ yj+2k and…

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Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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Q: Evaluate the triple integral II. x* dV, where T' is the solid tetrahedron h vertices (0, 0, 0),…

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Q: According to the divergence theorem, one of the following integrals represents the surface integral…

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Q: 6. Evaluate the triple integral ry dV where E is bounded by the parabolic cylinders y = x² and r =…

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

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Q: need to find the limits of integration in terms of ρ, φ, and θ.

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Q: Evaluate the line integral Sa y dx +z dy, where C is the line segment from (4) (-1, 1, 2) to (2,3,…

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Q: (1) Evaluate the double integral L V² + y² +1 dA where D is a quarter disk of center O(0,0) and of…

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Q: Evaluate the triple integral III xy dV where E is the solid tetrahedon with vertices (0, 0, 0),…

A: The given integral is, ∫∫∫E xydV Here E is the solid tetrahedron with vertices O0,0,0, A10,0,0,…

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: 7. Use Green's Theorem to compute the line integral | ry? dx – x² dy, where C is the triangle with…

A: ∫xy2dx - x2dy triangle vertices are (0,0), (2,0), and (2,2)

Q: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

Q: 1.) Set up the integral ||[ f (x,y,z)dV using a single triple integral where E is E the solid in the…

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Q: 1. Verify Green's theorem in the plane for 6 (3x- 8y) dx + (4y – 6xy)dy, where C is the boundary of…

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Q: Evaluate the triple integral. 5xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A: The point of intersection of the cylinder x=y2 and y=x2 is 0 and 1.

Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

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Q: Use Green's theorem to evaluate the closed line integral: . x²y dx +x'y dy along C between -1 < x< 2…

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Q: 4) Using Green's theorem, convert the line integral f(6y² dx + 2xdy) to a double integral, where C…

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