Page: 100 EXERCISES 2.10 1. Use Stokes' Theorem to evaluate F.dr_ for F=(xz,-y,x²y), where C is the boundary of the open surface, S that is bounded by x 0, y 0 and 2x+y+2z=8, which does not include xy- plane.

Q: (i) Use the Divergence Theorem to calculate the surface integral ſſ F-dS; that is, calculate the…

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Q: Let S be the portion of the cylinder y = ln x in the first octant whose projection parallel to the…

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Q: 386. Use the divergence theorem to calculate surface integral F-dS, where F(x, Y, z) = xªi – a³z²j+…

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Q: Q3// A surface S is defined by 2x2 + z = 1 and the bounded by the planes y = 0,y 2, x 0,z = 0 in the…

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Q: Q2// A surface S is defined by x2 + z = 9 and the bounded by the planes y = 0, y = 1,x = 0,z = 0 in…

A: Given that V=xy2z And y=0, y=1,x=0,z=0 The given surface is x2+z=9 The integral formed is,…

Q: (a) Evaluate ([ Á.ds where A=(x+y²)î-2xj+2yzk and s is the surface of the plane in the first octant…

A: For the detailed solution of the problem follow the next steps.

Q: Use Stokes' Theorem to evaluate F.dr for F=(xz,-y,x²y), where C is the boundary of the open surface,…

A: Given : vector field F=xz,-y,x2y and C is the boundary of the open surface, S that is bounded by…

Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

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Q: Find the flux ofF across the oriented surface S' by evaluating the surface integral F.î dS. F = zî +…

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Q: Find the surface area of that portion of the surface z = V4 -x that lies above the rectangle R in…

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Q: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

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Q: Use Stoke's theorem to evaluate the integral xydx +2x 'dy-&r 'zdz where C is the boundary of the…

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Q: EXERCISES 2.10 1. Use Stokes' Theorem to evaluate E.dr for F=(xz,-y,x²y), where C is the boundary of…

A: Given: F=<xz,-y,x2y> C surface, S is bounded by x=0, y=0 and 2 not include xy-plane Now,…

Q: Find the flux of F across the oriented surface S by evaluating the surface integral F.î dS. F = zî +…

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Q: Let R denote the solid in the first octant bounded by the planes 2x + 6y + 3z = 6, x = 0, y = 0, z =…

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Q: This means we can use the Divergence Theorem to find the flux  Let S be the surface of the portion…

A: Solution...

Q: 13. Calculate the flux of F across S.F = (3x, xz, z2) and S is the surface bounded by the paraboloid…

A: Given vector field is  F=3x,xz,z2 we have to find the flux through F where S is the surface bounded…

Q: Use Stokes' Theorem to evaluate [F•dF.C is the boundary of the portion of :=5-x² - y above the…

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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: 2.8 Using the divergence theorem, show that the volume, V, enclosed by the surface I can be obtained…

A: As per the Gauss Divergence Theorem, the surface integral of the normal component of G vector…

Q: Use divergence theorem to evaluate F •dš where F(x,y, z) = (2x + yz)ī + 2yzj – z?k and S is the…

A: According to the divergence theorem ∬SF¯·ds¯=∫V∇·F¯dV, where V is the volume bounded by the closed…

Q: Let C be the curve intersection of the sphere x'+y+=9 and the cylinderx+y° =5 above the xy-plane,…

A: To Evaluate: ∫CF·dr Using Stoke's theorem. where F→=<2yz,5xz,lnz> and C is the curve of the…

Q: Evaluate double integral f.ns where F=xi-yj+(z2-1)k and s is closed surface bounded by the planes…

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Q: Q2// A surface S is defined by x2 + z = 9 and the bounded by the planes y = 0, y = 1,x = 0,z = 0 in…

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Q: Q3// A surface S is defined by 2x2 + z 1 and the bounded by the planes y = 0,y 2, x = 0,z = 0 in the…

A: A surface S is defined by 2x2+z=1 which is bounded by the planes y=0, y=2, x=0, z=0 in the first…

Q: EXERCISES 2.10 1. Use Stokes' Theorem to evaluate F.dr for E = (xz,-y,x²y), where C is the boundary…

A: Applying stokes theorem we solve it

Q: Verify Stoke 's Theorem for F = (x² +y – 4) î + 3 xyj + (2 xz + z²) k over the surface of hemisphere…

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Q: 17 The solid bounded by the surface y =x² and the planes y+z=4 and z = 0.

A: To find the volume of the solid

Q: Integrate G(x, y, z) = x - y - z over the portion of the plane x + y = 1 in the first octant between…

A: Given G(x,y,z)=x-y-z

Q: Use Štoke's Theorem to evaluate the line integral - 2ydx +-6zdy + dz where C is the intersect | of…

A: Strokes theorem is ∫CF→.dr→=∫∫S∇×F→.N→dS=∫∫ScurlF→.N→dS x=rcosφy=rsinφ

Q: Let S denote the part of the cone z = Vx2 + y? that lies between the surfaces z = 2 + sin(xy) and z…

A: Given : S denotes the part of the cone z=x2+y2 that liesbetween the surfaces z=2+sinxy and…

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: 8. Use the divergence theorem to evaluate the flux integral OF-nds where F(x,y.z)= (x' +…

A: Given: F (x, y, z)= x3+cotan-1(y2z3), y3-ex2+z3, z3+ln(x-y)  n is the outward unit normal to S, and…

Q: What is the surface area of the portion of the surface z=x2+y that lays over the triangle on xy-…

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Q: Calculate ( (2x + y) dV , where V is a closed space bounded by the cylinder z = 4 – x? and the…

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Q: (a) Let S be the surface z2 = x² + y? bounded between the planes z = 0 and z = 2. Evaluate (z –…

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Q: Express the surface integral as an iterated double integral by using a projection of S on the…

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Q: Q4// A surface S is defined by x2 +z = 1 and the bounded by the planes y = 0,y = 2,x 0,z = 0 in the…

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Q: Let S be a square plate with boundary C, having each side of length 2 units, lying in the plane x =…

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Q: Evaluate || F:ñ dS where S is the surface bounded by z = a - Vx² + y² and the xy-plane including the…

A: The vector field is F→=xπ, yπ, 3z-2π. The surface is bounded by z=a-x2+y2 and xy-plane. The function…

Q: 8. Use the Divergence Theorem to calculate the surface integral for F(x, y, z) = (x³ +y³)i+ (y³ +…

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Q: Calculate dS where F = (e* sin y, e" cos y, yz²) and S is the surface of the box bounded by the…

A: We need to find the surface integral. We will need basic knowledge of parametrization of vector…

Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

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Q: 2y do over the surface S: z = ; 0<x< 2, 0<y<3 Evaluate

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Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,2x]. y = sinx 1 3 4 5 1 1 2…

A: Let's find.

Q: (2) Let S be the surface of the sphere of radius 4 centered at the origin oriented away from the…

A: We can apply divergence theorem to find this

Q: Verify Stoke's theorem for F = -2yzi + vj +3xk over the surface defined z = 5- x² -y? above the z=1…

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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: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…