2. When F = (y z, xz, x² y?) and S is the part of the paraboloid z = x? + y? that lies in the cylinder x2 + y² = 1, use Stokes' Theorem to evaluate curl F n ds

Q: Suppose f(x, y, z) = (a) As an iterated integral, 1 x² + y² + z² and W is the bottom half of a…

A: Triple integral

Q: For F(x,y,z) = (6y-4xz/(z2+1)2)i + (-2yz-6x/(z2+1)2)j + (-3/z2+1)k,  Calculate the net flux through…

A: consider the equation

Q: Let F(x, y, z) = 2yzi+ 4.xzj+ e*yk, and let C be the circle x2 + y² = 16, z = 3, oriented…

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Q: 2. Let D = 2xyā, + 2(x² + z²)d, + 4yzd, C/m² and evaluate surface integrals to find total charge…

A: given D→=2xy ax→+2x2+z2 ay→+4yz az→ it is known that ρ=∇·D→ it is known that…

Q: Let S be the cylinder x +y a, 0szsh, together with its top, x +y sa, z=h. Let F= -7yi + 7xj + 7x k.…

A: Given data: S is the cylinder, with its top x2+y2≤a and height0≤z≤h. Also Given a vector F→ Such…

Q: Evaluate : //| cos(x² +y³) dV, where E is the region bounded by the disk x² + y? < 9 E and the plane…

A: From the region of integration which is bounded by x2+y2≤9 and z=1, identify the limits of x, y and…

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 e dV where E is enclosed by the paraboloid z = 2 + x² + y°, the cylinder z² + y² = 2, and…

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Q: (e) If E C R³ is the ellipsoid (x/2)2 + (y/3)² + (z/4)² = 1 and F evaluate the integral ffE curl F-…

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Q: (2) Use Stoke's theorem to evaluate the integral curl where S is the surface given by 2= et-- - 1, 2…

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Q: 2)use the polar coordinates to evaluate the double integral : A) || Vx2 + y² dA , R is the disk x² +…

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Q: Prove that the integral of the bottom of a half ellipsoid, (x/a)^2 + (y/b)^2 + (z/c)^2 =1, is equal…

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Q: Evaluate the surface integral. y ds S is the part of the paraboloid y = x² + z² that lies inside the…

A: The projection of S onto the xz-plane is the disk D=x,z: x2+z2≤9. We have to calculate the surface…

Q: Evaluate the triple integral ||//. z°e" dV where E is bounded by the parabolic cylinder z = 16 – y?…

A: The volume of a solid can be calculated using the triple integrals. The unit dV can be written as…

Q: (9) Evaluate the surface integral / S, czdS, where o is the part of the plane r+2y+3z = 6 that lies…

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Q: Evaluate // e² dV where E is enclosed by the paraboloid z = 2 + x² + y², the cylinder E x² + y? = 3,…

A: Since we are given with the multiple number of questions and answered according to the guideline.

Q: Use Stokes' Theorem to evaluate | F - dr, where F (x, y, z) = zi + yj – xk and C is the 9 – z? y? in…

A: Given F→x,y,z=zi^+yj^−xk^ We have to evaluate ∫CF→⋅dr→,where C is the boundary of the part of the…

Q: The double integral I = °S x2 + y? dydx in polar coordintes is:

A: Given integral is I=∫13∫1xx2+y2 dydx We have to change the given integral into the polar coordinate…

Q: Evaluate the surface integral of D enclosed by the rectangular parallelepiped formed by the planes x…

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Q: Change the Cartesian integral into an equivalent polar integral: V1-x? STf(x, y) dydx -1º-V1-x? 2n ]…

A: Consider the cartesian integral         ∫-11∫-1-x21-x2fx,y dy dx Convert it into polar integral.

Q: Evaluate the following surface integral. ∫∫S (1 + yz) dS; S is the plane x + y + z = 2 in the first…

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Q: Evaluate the surface integral SP ( – 2) // where S is the portion of the cylinder r2+22 = 1 above…

A: It is given that S is the portion of the cylinder x2+z2=1 above the xy plane between y=1 and y=2.

Q: 9. If F = (x – z) î + (x³ + yz)ĵ + 3xy² k and S is the surface of the cone z = a – Va? +y?) above…

A:

Q: Let F = . Use Stokes' Theorem to evaluate / curlF · d5, where S is the hemisphere x² + y² + z² =…

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Q: Use either form of Green's Theorem to evaluate the following line integral. $9x²1² 6 C $9x³y² dx +…

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Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = x2z2i + y2z²j + xyzk, S is the part of the…

A: Given: F(x,y,z)=x2z2i+y2z2j+xyzk   and S is the part of the paraboloid z=x2+y2 that lies inside the…

Q: Use Stoke's theorem to compute the integral SL(V × F) · n dS, where F(x, y, z) = (xz, yz, xy) and S…

A: We have to compute ∬(∇×F)·n dS , where F(x,y,z)=(xz,yz,xy) and S is the portion of the sphere…

Q: Evaluate the surface integral. (z + x2y) ds S is the part of the cylinder y2 + z2 = 16 that lies…

A: Given ∫∫S(z+x2y)dS where S is the part of the cylinder y2+z2=16 that lies between the planes x=0 and…

Q: Use Stokes' theorem to evaluate curl F. dS, where F(x, y, z) = e*Y cos(z)i + x²zj + xyk, and S is…

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Q: Calculate the surface integral S FdS, where S is cylinder r² + y = 1, 0 + yz, 3 =

A:

Q: Use Stokes' Theorem to evaluate ∫∫ s  curl F. dS  F(x,y,z) = x2 sin zi +y2 j +xyK, S is the part of…

A: Given: F(x,y,z)=x2 sin z i + y2 j +xy k and S is the surface of paraboloid z=1-x2-y2, which is above…

Q: (b) Evaluate the surface integral S.S x² dS over the surface x² + y² = 1 between z = 1 and z = 4.

A: x=cos(u), y=sin(u), z=v  0≤u≤2π, 1≤v≤4 S(u,v)=&lt; cos(u), sin(u), v &gt;

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: 3) Use Stokes theorem to evaluate (| curl F-ndS. where F= (xyz, x, e" cos z), while S is a surface…

A: r(t) is the vector function for C, the curve around the base of the hemisphere (and therefore the…

Q: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x? + y?…

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Q: If S c R³ is the unit sphere and F Sls curl F n dS. (e*y, sin(22 + y), xyz), then evaluate the…

A: We will find out the required value.

Q: Let F < ryz, ry, r'yz Use Stokes' Theorem to evaluate curlF dS, where S consists of the top and the…

A: The given surface is a cube, where the bottom face is not considered. The surface in question has 4…

Q: Use either form of Green's Theorem to evaluate the following line integral. 03x y dx+ 4x y dy; C is…

A: According to the given information, it is required to find the value of integral using Green’s…

Q: Use Stokes' theorem to evaluate f curlF · ds. F(x, y, z) = y²zi+xzj + x²y²k S is the part of the…

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Q: Evaluate the surface integral. z2 ds, S is the part of the paraboloid x = y2 + z? given by 0 < x < 1

A: Evaluate the surface integral.

Q: (b) Use Stoke's Theorem to evaluate the line integral $ (3? – 22) dr + (z² – x²) dy + (y² – x²) dz,…

A: Stokes theorem  ∮CF.dr=∫∫SCurl F .dS Where S be a smooth surface that is bounded by a  closed,…

Q: . Evaluate the flux integral f. curl (z cos xi+ yj+ x sin y k) dS where S is the part of the outward…

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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: Assume that S is the disk 2 + y² <4 in the plane z 0 oriented upwards with positively oriented…

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Q: Find the surface integral (x + y²)dS when S is the cylinder x² + y² = 4,0 < z < 5.

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Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

A: Given problem:- Evaluate the ∫∫∫E z dV, where E is bounded by the cylinder y2+z2=4 and the planes z…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x? + y?, the cylinder x? + y? 5, and the…

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Q: Verify that both integrals in Stokes' Theorem are equal when F= (y – 2, z – 1, r – y), S is the cap…

A: Solve

Q: 2). Use Stokes' theorem to evaluate the integral 6 F • dř for F(x, y, z) = (x – y)î + (y – z)ĵ + (z…

A: Formula: By Stoke's theorem we have ∮C F · dr¯  =∫t=t1t=t2 F¯(r(t))r'(t) dt, where r(t) is…

Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = xyzi + xyj + x²yzk, S consists of the top…

A: The given problem is to evaluate the surface integral using stokes theorem where S is the surface of…