Evaluate the surface integral F. dS where F = (4x, -5z, 5y) and S is the part of the sphere x² + y + z? = 16 in the first octant, with orientation toward the origin. SLF. dS = 512pi/3

Q: Evaluate the following surface integrals: Vx² + y² from + y2 + z2 dS, o : the part of the surface of…

A: surface integral along the surface S given by z=g(x,y)  ∫∫Sf(x,y,z)ds=∫∫Df(x,y,g(x,y))dx dy  Where D…

Q: Evaluate the surface integral LL 6xzdS where S is the part of the plane 2x + 2y + z = 4 that lies in…

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Q: Evaluate the surface integral fs F. dS where F = (4x, -2z, 2y) and S is the part of the sphere x² +…

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Q: Evaluate the surface integral f F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x2 +…

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Q: Evaluate the following surface integrals. (a) || Vzds where S is the surface of the sphere a? + y? +…

A: According to the Bartleby guidelines, we can answer only one question per request, so, I'm solving…

Q: Set up, but do not evaluate, an iterated integral that equals the surface integral |/ (2² – y²) dS,…

A: Given data:   The given surface integral is I=∫∫S(z2-y2)dS. The given part of the cone is…

Q: Evaluate the surface integral SS (y) dS, where S is the surface z = x + y^2 for 0 ≤ x ≤ 1 and 0 ≤ y…

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Q: Evaluate the surface integral. z + x2y x²y) ds S is the part of the cylinder y² + z2 = 9 that lies…

A: We have to find the surface integral from the given condition

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

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Q: Evaluate the surface integral. dS S is the part of the sphere x2 + y² + z? = 16 that lies inside the…

A: The objective is to find the surface integral  ∫∫Sy2dS  where S is the part of the sphere…

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

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Q: Compute the triple integral f(x,v.z)dxdydz where D is the sphere with center O and radius R and…

A: Given that ∭Df(x,y,z)dxdydz where f(x,y,z)=R2-(x2+y2+z2). By the spherical coordinates,…

Q: Evaluate the surface integral: S Ssx*y ds Where S is the surface of the paraboloid z = 4 – x2 – y?…

A: To evaluate the given surface integral, use the following formula. ∬SFx,ydS=∬DFx,y1+∂z∂x2+∂z∂y2dxdy

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

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Q: Evaluate the surface integral  ffR(x+y)dS where σ is the portion of the plane z = 6 − 2x − 3y in the…

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

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Q: Find the surface integral ls yz dS, where S is the plane surface z = x + 3y lying above the…

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Q: Evaluate the surface integral. 2,2 ds S is the part of the cone + y that lies between the planes z =…

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

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Q: * Evaluate the surface integral SS F - d§, where F = z7 + y²7 + z² and S is the boundary of the…

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Q: Use Stoke's theorem to calculate the surface integral || F. dS, where S F(x,y. =) = (* siny)i+ (e*…

A: Consider the provide question,

Q: Suppose that S is the upper half of the hemisphere of radius 1, oriented upward. Recall that S is…

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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: 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: Evaluate the surface integral IL (1+ 2)ds, where S is the hemisphere z = V1 – x² – y². -

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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: Evaluate the surface integral of G(x, y, z) = z - y over the surface S, where S is the portion of…

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Q: find the exact area of the surface obtained by rotating x=t^3,y=t^2, 0<t<1 about the x-axis.

A: y=t^2 so t= sqrt(y)x=t^3= (sqrt(y))^3 = y^(3/2)x=y^(3/2) (graphed this equation)

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

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Q: Choose the correct integral to evaluate the surface integral (x+y)zdS,where S is the portion of the…

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

A: Given: The surface integral is given as, S is the part of the cone z2-x2 + y2 that lies between the…

Q: Find the surface in the accompanying area of the heli r(r,0) = (rcos0)i+(r sin 0) j + Ok, 0s0<2r,…

A: Introduction: The formula for the surface area of the function r(r,θ) is given by,…

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 . xz? dS; where S is the part of the surface y = x² + 2z R= {(x,…

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Q: Use Gauss's Theorem to find the surface integral OF •dS across the positively-oriented S sphere of…

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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: Evaluate the surface integral , F· dS where F = (4x, –4z, 4y) and Slis the part of the sphere x2 + y…

A: Answer

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: (a) Compute the surface integral || a xy dS, where S is the quarter cylinder x2 + y? = 1; x, y > 0…

A: Given that The surface integral is ∬Sxy dS, where S is the quarter cylinder x2+y2=1; x,y≥0 between…

Q: Evaluate the surface integral f, F. dS where F = 3xyi + 9x²j+3yzk and S is the surface z = xe", 0≤x≤…

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Q: 6. Evaluate the surface integral where o is the portion of the cone z = Vr? + y? between the planes…

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Q: Convert the triple integral GyaldV+o spherical coordinates. Eis the Salid that lies within the…

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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: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

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Q: Evaluate the surface integral fSs x dS, where S is the cylinder y²+z² = 4 between (2) the planes x =…

A: We have to evaluate the surface integral

Q: Evaluate the surface integral [(xz + y* ) ds where s is the surface of the XZ- cylinder y + z? =…

A: Consider the provided question,

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

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Q: Evaluate the following surface integrals: (a) x + y) ds, o : part of the surface 2x + 3y + z = 6 in…

A: To calculate the surface integral, first we write the equation of the surface in the form…

Q: Evaluate the surface integral s F. dS where F (-x, -4z, 4y) and S is the part of the sphere x? + y?…

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