10. Evaluate the integral [F·ñdA where F = [2x+z, y+z, x+3z] and S is the surface of the box x² + y² +z² ≤4 S

Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

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Q: Use Green's Theorem to evaluate the line integral § 2y² dx + 3x² dy, where C is the boundary of the…

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Q: 2 Find the area of the portion of the paraboloid x=9-y²-z² that lies above the ring 1 ≤y² + z² ≤ 9…

A: Given, The paraboloid y = 9-y2-z2  above the ring 1≤y2+z2≤9 in the yz plane.

Q: 6. Let F(x,y, z) = x²i+ j+k Use Stoke's Theorem to evaluate ſſ. (V × F) · n dA, where S is the open…

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Q: (b) Prove that Vx, y ≤R : x² + xy + y² ≥ 0, and that x² + xy + y² = 0 if and only if x = y = 0.…

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Q: Evaluate [[ 4.ry² — 5x + 5y³ dA over the rectangle R = {(x, y) : -1 ≤ x ≤ 2 and − 1 ≤ y ≤1}.

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Q: 3. Verify Gauss Theorem in evaluate ff F-n ds where F(x, y, z) = 4xzi - y²j+yzk and σ is the surface…

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Q: Use Lagrange's multiplier(s) to find the maximum and minimum for f(x, y, z) = x² + 2x + 2y2 + 3z2 on…

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Q: Evaluate | F dr where Cis the intersection of the surfaces y =x' and z =x' from the origin to…

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Q: · ƒ [‚²³ · F . S F = (4x³z, 4y³z, 3z¹) Calculate dS where and S is the surface of the solid bounded…

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Q: 10. Let D be the parallelogram spanned by the vectors (3, 4) and (5, 1). Apply the change of…

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Q: 3. Let H = 2xi – 3xy j+xz² k. Calculate ſ, Ĥ •d where S is the surface of the cube with corners at…

A: Given- Let H→ = 2xi→ - 3xyj→ + xz2k→ To find- Calculate ∫SH→·dA→ where S is the surface of the cube…

Q: Let S denote the surface of the box [-2,3] x [-4,2] × [0,3], ori- ented outward, minus the disc that…

A: Given that the surface S denotes the box [−2,3]×[−4,2]×[0,3].The orientation is outward and the…