5- Evaluate the surface integral ffs G(r)dA, where G = arctan(y/x) and S is the surface z = x2 + y²,0< z < 9,0 < x,0 < y.

Q: Evaluate the tripple integral of f(x,y,z) = sin(x2+y2)  over the solid cylinder with height 5 and…

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Q: Evaluate the surface integral.     Sz2 dS, S is the part of the paraboloid  x = y2 + z2  given by…

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Q: Use Green's Theorem to evaluate the line integral. dx + (2 + x) dy -y2/2 - C: boundary of the region…

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Q: Jse Green's theorem to evaluate line integral | V8 + x3 dx + 9xy dy where C is a triangle with…

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Q: 3. Set up (do NOT evaluate) the iterated double integral equal to the surface area of the portion of…

A: Given that  the portion of the parabolic cylinder z = x2  We have to set up the iterated double…

Q: 7. Evaluate the line integral f, F· dr where F(x,y, z) = x³i – y²j+ zk and C is the x2 + 2xy + y²…

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Q: Calculate the integral I = = • (y² + z²) dx + (z² + x²) dy + (x² + y²) dz where I is 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: (b) A solid G is bounded above by x² + y² + z² – 4z – 12 = 0 and below by z = Vx² + y². Sketch the…

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Q: Evaluate line integral I=∫_c▒〖x^3 ydx+(x+2y)dy〗 over a part of parabola y=x^2 from (0,0) to (1,1) by…

A: Introduction: The line integral is an integral when the integral is performed along a curve or a…

Q: (b) Set up a definite integral that is equal t length of the portion of the parabola y which serves…

A: Introduction: The washer method is used to calculate the volume enclosed by two functions. In this…

Q: Calculate the line integral x y dx + x² y³ dy where C is the triangle with vertices (0,0), (1,0),…

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Q: 5. Use our Early Parameterization step by step including sketch of the surface to evaluate the…

A: Given that The equation of cylinder in the xz-plane as x2+z2=1 Also, the given surface integral lies…

Q: 3 Use polar coordinates to evaluate the integral (3) f[/x² +y° dA Ris bounded by the semicircle y =…

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Q: The surface area of the surface generated by revolving y=1-x² for 0<x<1 about the x- axis is s=…

A: If you like the solution then please give it a thumbs up.... The Answer is:              S =…

Q: 2. Let S be the surface x² + y² = (2-2)², y Evaluate Jl F = (2x+y-xz, -x, -(2 — z)²), choosing a…

A: Using parametrization of the surface S

Q: 1. Let a be a positive number. Find the surface area of the solid obtained by revolving the curve…

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Q: 387. Use the divergence theorem to calculate surface integral F. dS when F(x, y, z) = x²z³i+ 2xyz³j+…

A: Given that: F(x,y,z)=x2z3i+2xyz3j+xz4k and S is the surface of the box with vertices (±1,±2,±3).

Q: Evaluate SſF-dš where F = yi +2x j +(z-8)k and S is the surface of the solid bounded by 4x + 2y +z =…

A: By using the divergence theorem we solve the above question

Q: 4.) Write a double integral that cepresents the surface R. cegion the double that lies obove the to…

A: Identify the limits of integration from the region. Here, the region is a triangle which is bounded…

Q: 1. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

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Q: #3. Set up the iterated integral to evaluate the triple integral (x² +, yz) dV, E where E is the…

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Q: How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the…

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Q: 5- Evaluate the surface integral SS,G(r)dA, where G = arctan(y/x) and S is the surface z = a² + y²,0…

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Q: 2. Evaluate the surface integral f, (curlF) · n dA directly for the given F and S, F =…

A: Here we have to surface integral ∬s(curlF).n dA

Q: a) Evaluate the surface integral 2x²y dS over the surface y² + z² = 1 between x = -1 and x = 5.

A: Evaluate the surface integral ∫∫δ 2x2y dS over the surface y2+z2=1 between x=-1 and x=5. If ru, v is…

Q: 5. Evaluate [[ F • dS where F(x,y,z)= and S is the boundary of the solid region E enclosed by the…

A: Given: Evaluate  ∬S F. dS  Here, F(x, y, z) = &lt;y, x, z&gt; S is the boundary of the solid region…

Q: .2 Evaluate the line integral xy dx + x-dy, where C is the path going counterclockwise around the…

A: Given, ∮Cxydx+x2dy, Where C is the path going counterclockwise around the boundary of the rectangle…

Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y…

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Q: An iterated double integral for evaluating the surface integral S f,(xy+yz) dS where E is the part…

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Q: 9) Consider the solid Q bounded by the surfaces: S₁: x1 = (z −2)², S₂: y+z=2, S3: x=0, S₁: y=0, S5:…

A: The first surface given is as follows: S1: x-1=z-22⇒x=1+z-22⇒dx=2z-2dz The function given is Fx, y,…

Q: (3) Evaluate the flux integral where S is the surface given by 22 =r + y², 0< z< 4, oriented upwards…

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Q: Evaluate triple integral(E) (1/((x^2+y^2+z^2)^3/2)) dV where E is the solid bounded by the planes x…

A: Given the solid is bounded by the planes x=0, y=0 and z=0 and two spheres with radii 1 and 3.…

Q: Flux Integrals (sin y cos zi+e² cos zj+cos y ln(1+x²)k) ·N dS, where S is the sphere x2 +y? + z² = 1…

A: Consider the equation

Q: . Apply Green's Theorem to evaluate the given integrals: a. 2x +y)dx + (2xy = 3y)dy where Cis any…

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Q: b)Consider the graph of y = (2x − x^2)^1/2 on the interval 0 ≤ x ≤ 2. Compute         the area of…

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Q: Evaluate the surface integral F*n d-sigma where F = -4xyi + 10x^2j - 4xyzk and S is the surface z =…

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Q: oply Green's theorem to evaluate the line integral fxydx - xydy, where C is the boundary of the…

A: See the attachment

Q: 1. Evaluate the surface integral [[' xz² ds ; o is the part of the cone z = x² + y² that lies…

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Q: Q2- Evaluate the triple integral fSS 6xydv , on the region Q Where Q is the tetrahedron bounded by…

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Q: 3. Find the volume of the solid under the plane 3x+ 2y – z = 0 over the shaded region between the…

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Q: integrate the given function over the given surface. H(x, y, z) = x2√(5 - 4z), over the…

A: Application of integration: We can use cylindrical coordinate to find a parametric equation for the…

Q: 5) Using Green's theorem, convert the line integral f.(6y² dx + 2xdy) to a double integral, where C…

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Q: V1 – ² dadydz where E is the solid limited from below the cone Calculate the integral E x² + y2 and…

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Q: 3. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

A: 1st we need to convert the curve in x=f(y) form and corresponding limits for y , Then use given…

Q: Cvaluate AP G is a solid in the first octant bounded by the plane y+ z = 2 and the urface y = 1 -…

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Q: 3. Evaluate the triple integral || ryz dV; G is the solid in the first octant that is bounded by the…

A: To evaluate the given integral ∫∫∫Gxyz dV. The limits are given as  z=0 to z=2-x2 and y=0 to y=x and…

Q: 2. Consider the triangle {(x, y)| x, y > 0, 2x + y < 1}. Let C be the boundary of this triangle…

A: Given triangle is x,y:x,y≥0,2x+y≤1. Let C be the boundary of this triangle oriented in the…

Q: EXAMPLE 4 Line integral as a double integral Evaluate (4x³ + sin y²) dy – (4y³ + cos x²) dx, where C…

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Q: An integral that allows determining the value ofS,ƒ · dr,where F (x, y, z) = (-xz, yZ y), is: IT…

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