Evaluate the following surface integrals: Vx² + y² from + y2 + z2 dS, o : the part of the surface of the cone z = z = 0 to z = 1. (b)

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: 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: Evaluate the integral for y'dx + z?dy + x²dz, where C is the triangular closed path joining the…

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

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

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

A: Stokes theorem:  Let C be a closed curve S be a surface enclosed by curve C. F is defined every…

Q: Evaluate the surface integral (x - z) dS where S is the portion of the cylinder r +z? = 1 above the…

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Q: Evaluate the surface integral. x dS, S is the triangular region with vertices (1, 0, 0), (0, –2, 0),…

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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 generated by rotating y=sin x. 0 ≤ x≤ π about the x-aixs.

A: Area of surface problem....

Q: Use cylindrical coordinates to evaluate the integral 2²dV where E is the solid that lies within the…

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Q: Set up, but do not evaluate, the integral for the surface area of the solid obtained by 3x rotating…

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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 triple integral. II (x - y) dV, where E is enclosed by the surfaces z = x2 - 1, z = 1 -…

A: Calculate the points of intersection of the curves, x2-1=1-x22x2=2x2=1x=-1,1 According to the…

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: Compute the surface integral // xy dS, where S is the quarter cylinder x² + y² = || S 1; x, y > 0…

A: Given surface S is the quarter cylinder x2+y2=1, Where x,y≥0 between z=0 and z=4 We have to…

Q: Compute the surface integral over the given oriented surface: F = y²i+6jxk, portion of the plane x +…

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Q: Let o be the portion of the surface y² = x that is between the horizontal planes: z = 0 and z = 4…

A: the portion of the surface y2 = x that is between the horizontal planes: z = 0 and z = 4 and is…

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: 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: Consider the region formed by the graphs of y = e^x , y =0 , x = 2 and x = 4. Which integral…

A: We sketch the region using a graphing calculator The shaded region is rotating about the y-axis The…

Q: Evaluate the triple integral W z dV where E is the solid bounded by the cylinder y² + z² = 100 and…

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Q: Set up the surface integral for upward Flux of the upper hemisphere of radius = 5 (z20) such…

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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: 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: 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: Calculate the following surface integral over the surface given by x2 + y = 16, 0 <z<4, and f(x, y,…

A: Given surface x2+y2=16,   0≤z≤4 and fx,y,z=e-z Surface integral =∫∫Sf.ndS Here, limits of z are…

Q: Calculate the points of intersection of the curves x² = 4y and aup ert neswted biloa ent to y²/4 = x…

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Q: Compute the surface integral over the given oriented surface: F = (0,0, e+z), boundary of the cube 0…

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Q: SET UP ONLY the iterated double integral in polar coordinates that give the volume of the solid…

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Q: 18. z = 4 – x2 – y², 0<z< 3; f (x, y, z) = x² / (4 – 2) - -

A: Use polar coordinates to solve the integral

Q: Use spherical coordinates to evaluate the triple integral where E is the region bounded by the…

A: Solution :-

Q: Evaluate the triple integral x dV where G is the solid that lies below the surface z = 15xy and G.…

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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…

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Q: a.) Find the area of the surface defined by 4x + 2y + z = 1, x² + y? < 1. b.) Evaluate the integral

A: Surface area

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: Express the double integral || (x +1)dA, where 2 is the region in the upper half- plane (i.e. y20)…

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

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Q: set up an integral that representsthe are of the surface obtained by rotating the curve x=2t2+1/t…

A: To determine the integral representation of the area of the surface that is oriented by rotating the…

Q: By transforming into triple integral, evaluate J] (& dy dz +xy dz dx +xz where S is the closed…

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Q: Find the integral of the function f(x,y, z) = x² + y – 2z surface of the unit sphere. over the

A: To find- Find the integral of the function fx, y, z = x2 + y - 2z over the surface of the unit…

Q: 1. Evaluate the following surface integrals: (a) (x + y) dS, 0 : part of the surface 2x + 3y + z = 6…

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Q: Use spherical coordinates to evaluate the tripple integral      Where E is the reigon bounded by…

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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 triple integral zdV over the solid region E enclosed by the two surfaces z= 4/x² + y?…

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Q: Find the exact area of the surface obtained x=t°, y =t 0<t<lby rotating about the x- аxis.

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