Evaluate the surface integral. [6 ( ² + x²y) ds S is the part of the cylinder y2 + z² = 9 that lies between the planes x = 0 and x = 6 in the first octant

Q: [(x + y + 2) ds, (x+y+z) ds, S is the parallelogram with parametric equations x = u + v, y = u - v,…

A: see my solutions

Q: a) Find the value(s) of (1+ i)2/3.

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Q: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…

A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…

Q: 1. Use Green's theorem in order to compute the line integral $ (3cos + 6y?) dx + (sin(5") + 16x³) dy…

A: Here the given integral is                               ∮C3cosx+6y2dx + sin5y+16x3dy

Q: Apply Green's Theorem to evaluate the integral. $(4y + x) +x)dx + (y + x)dy C: The circle (x-3)² +…

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Q: Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin,…

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Q: luate the surface integral. // (x + y + z) ds, S is the parallelogram with parametric equations x =…

A: Sub x= u+v  y= u-v  z= 1+2u+v

Q: Find the average height of the paraboloid z = x+y over the square 0sxs1, 0 sys1. The average height…

A: Here in this problem we are given                                      z=x2+y2  ,0≤x≤1 and 0≤y≤1We…

Q: Compute the surface integral s F-ndo. F = xyi - x¹j+ (x+z)k. The surface is the top of the plane 2x…

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Q: Use a parameterization to find the flux SF-n do of F=2²i+xj-3zk in the outward direction (normal…

A: Draw the surface and parametrize the surface:

Q: The figure shows a surface z = 8(x² + y2) and a rectangle R in the xy-plane. ZA z = 8(x² + y²) R 3…

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Q: 2z Sc (2²+273 dz (z-w)³

A: CAUCHY THEOREM-: IF F(z) IS AN ANALYTIC FUNCTION IN A SIMPLY CONNECTED REGION ,THEN ∫cF(z)dz=0 ,…

Q: Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²)) 3+ (3x+4y+6e²²) k (a) Find curl F. curl F = (b) What…

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Q: Evaluate ∫ ∫ √ (x2+ y2) dA where R is the portion of the annulus 1 ≤ x2 + y2 ≤ 16 with y ≤ 0 using…

A: We have to evaluate the double integral.

Q: parametrization of the surface z = 3x² + 8x, ymbolic notation and fractions where needed.

A: In this question, the concept of the tangent plane is applied. The equation of the tangent plane of…

Q: Find a parametric representation for the surface S, where S is the part of the cylinder x2+y2 = 4…

A: A surface S where S is the part of cylinder x2+y2=4 which lies between z=-2 and y+z=2. To Find:…

Q: Find the point on the surface r – 2xy + 2y² – x+ y = 0 closest to the point (1, 2, –3).

A: Consider the provided question, We have to find the point on the given surface closest to the point…

Q: 1 x² dA, where R is the region enclosed by the circles x² + y² = 1 and x² + y² = e² + y² , by…

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Q: 2. Let F = (sin(22)e² - y²)i + (x² - cos z)j + (x²e³²)k. Consider the tetrahedron, oriented with…

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Q: 1 E x² + y² + z² 2 = 25 and x² + y² + z² Evaluate J x² + y² + z² dV, where E lies between the…

A: Given that the spheres,          x2+y2+z2=25, and x2+y2+z2=49, in the first octant.

Q: The paraboloid z = 3 - x - x² - 3y2 intersects the plane x = 4 in a parabola. Find parametric…

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Q: Evaluate the circulation of Gayi + zj+5yk around a square of side 9, centered at the origin, lying…

A: Solution :