Evaluate the surface integral. || x2yz ds, s is the part of the plane z = 1+ 2x + 3y that lies above the rectangle [0, 4] x [0, 2]

Q: Use Green's theorem to find the surface integral of the following geometry if V = xy'i - x³yi, and…

A:

Q: Evaluate the surface integral | f(x,y,z) dS using an explicit representation of the surface. S…

A: To evaluate the surface integral using explicit  representation of the surface of function…

Q: Evaluate the surface integral F. ds where F = 5xyi +8x²j+ 5yzk and S is the surface z = ïe², 0 ≤ x ≤…

A:

Q: Evaluate the surface integral DOUBLE INTERGAL of S −→F . d−→S , where S is the part of the cone z…

A: Given a vector field Fx,y,z=xi^+yj^+z4k^.  Now the surface integral for the vector field in the…

Q: Evaluate the surface integral F.n dA, where F(x, y, z) = i + j + z(x² + y²)<k and S is the surface…

A:

Q: 3) Evaluate the surface integral. I| (x²z+ y²z) ds where S is the part of the plane z = 4 + x +y…

A:

Q: 2. Evaluate the surface integral f,yz ds ; o is the part of the plane x + y + z = 2 that lies in the…

A:

Q: Evaluate the surface integral below where S is the cone with given parametric equations xzds ,wher S…

A:

Q: Evaluate the surface integral. (x²z + y²z) dS Is S is the hemisphere x2 + y2 + z2 = 9, z 2 0

A: Given:      ∫∫Sx2z+y2zdS    where S is the hemisphere x2+y2+z2=9 , z≥0   Parameterize the hemisphere…

Q: 5. Evaluate the surface integral S_(x+ y) ds ; o is the part of the plane 2x + y +z = 3 that lies in…

A:

Q: Evaluate the surface integral (x + y + z) dS where S is the part of a plane parametrized by S: r(u,…

A:

Q: Evaluate the surface integral [[ F.ds where F(x, y, z) = (x³ +y³) i+(y³+z³) j+(z³+x³) k S and S is…

A: We will calculate surface integral , use of divergence theorem

Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: Evaluate the surface integral. /| x*yz ds, s is the part of the plane z=1+ 2x + 3y that lies above…

A:

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

A:

Q: Evaluate the surface integral.∫∫S (x2+y2+z2) dS, S is the part of the cylinder x2+y2 = 9 between the…

A:

Q: Evaluate the surface integral| f(x.y.z) dS using an explicit representation of the surface. f(x.y.z)…

A:

Q: Evaluate the surface integral. z2 S is the part of the paraboloid x = y2 + z² given by 0 sx 5 4 1 V5…

A:

Q: Evaluate the surface integral. ∫∫sxdS, S is the part of the plane 6x+3y+z=6 that lies in the first…

A: The plane has intercepts at (1,0,0), (0,2,0), (0,0,6). The parameterize the surface S by. where

Q: -. Evaluate the surface integral z'/x2 + y?dS, where S is the surface parametrized by Ocoso, y =…

A:

Q: Find a parametric representation for the part of the cylinder y2 + z² = 36 that lies between the…

A:

Q: Evaluate the surface integral. x² + y2 + z• ds S is the part of the cylinder x2 + y2 = 25 that lies…

A: Given, Where, S is the part of the cylinder x2 + y2 = 25 which lies between the planes z = 0 and z =…

Q: Evaluate the surface integral. x²z² ds S is the part of the cone z² = x2 + y2 that lies between the…

A:

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

A:

Q: Evaluate the surface integral F. dS, where F(x, y, z) = xi+Yj+z k is taken over the paraboloid z = 1…

A:

Q: Evaluate the surface integral. J[x²³x² x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

A:

Q: Calculate the surface integral ∫ ∫ s F ∙ N dS where F (x, y, z) = -y2i + xj + k and S is the shaded…

A: We will find out the required surface Integral.

Q: Evaluate the surface integral fs F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x? +…

A:

Q: Evaluate the surface integral. y² ds, S is the part of the sphere x² + y² + z² = 1 that lies above…

A:

Q: Evaluate the integral for y*dx + z²dy + x²dz, where C is the triangular closed path joining the…

A: To evaluate the integral ∫Cy2dx+z2dy+x2dz where C is the triangular closed path joining the points…

Q: Which of the following represents the area of the surface cut from the plane z = ax + by by the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the surface integral || x2 z2 dS, where S is the part of the cone z2 = x² + y?, S that lies…

A: Here we solve the given problem of calculus.

Q: (a) Evaluate the following surface integral yex²+z² dS, where o is the portion of the surface of the…

A: Given the integral ∬σyex2+z2dS we have evaluate the given surface integral where σ is the portion of…

Q: Let o be the portion of the paraboloid F(u, v) = u cos(v)i+u sin(v)j+ u*k for which 0 < u< sin(v), 0…

A:

Q: Evaluate the surface integral: || G(x, y, z) ds for G(x,y,z) = z², where S is the portion of the…

A:

Q: Use Stokes's Theorem to evaluate f. F dř where F(x, y, z) = (x- y) i+ (y-z)j+ (z - x) k and S is the…

A:

Q: Evaluate the surface integral. ds 2 + y32), o s x s S is the surface z = x3/2 0sx < 1, 0 s ys2

A: Given,                        z = 23(x32+y32)and domain D : 0 ≤ x ≤ 1, 0 ≤ y ≤ 2.∂z∂x= 23(32 x) =…

Q: Evaluate the surface integral (4x² + 3y)dS where S is the part of the plane 2.x + 5y + z = 48 inside…

A: Surface integral is a general form of multiple integrals over a surface. Sometimes it is same as…

Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

A: Given ,x2+y2+z2 = 22       _________(I)and z = x2+y2     __________(II)Putting the value of z from…

Q: (b) Evaluate the surface integral ƒ (x, y, z)dS where f(x,y, z) = z² and S is a portion of the cone…

A:

Q: Evaluate the surface integral fF- dS where F = (52,-52, 5y) and S is the part of the sphere a² +2+22…

A: Solution

Q: Evaluate the surface integral. ∫∫s(x2 + y2 + z2) dS, S is the part of the cylinder x2 + y2 = 9…

A: To evaluate :  ∫∫s(x2 + y2 + z2) dS, S is the part of the cylinder x2 + y2 = 9 between the planes z…

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

A:

Q: Evaluate the surface integral of g(x,y.z) = z over the surface S, where S is the hemisphere x +y +z…

A: Detailed solution is given below.

Q: Jevaluate the surface integral ff, (y²z2 i+ z?x² j+ z²y²k).n ds, where S is the part of the sphere…

A:

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

A:

Q: Evaluate the surface integral. SS, xz ds, S is the part of the plane 2x + 2y + z = 4 which is in the…

A:

Q: The wedge cut from the cylinder, x? + y² = 1 by the planes, z = -y and z = 0. Use a tripple integral…

A:

Q: Evaluate the surface integral. v² as S is the part of the sphere x2 + y2 + z2 = 64 that lies inside…

A: A scalar function f(x,y,z) is a rule that is used to associate a number or quantity with a…

Q: Evaluate the surface integral. (x²z. y?z) as x2z + S is the hemisphere x2 + y2 + z² = 4, z 2 0

A: