Q#5. Evaluate the surface integral When f(x, y, z) = 3xyz and o is the portion of the plane x + 3y + 5z = 6 lying in the first octant.

Q: 2. Evaluate the triple integral //y o 2 = y, the xy-plane, and the parabolic cylinder y = 1- r2. y…

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Q: 1. Calculate the line integral f F-d7, where F (z. y, 2) = -y? +z3 +zk and C is the path C along the…

A: This is a problem from line integral.

Q: Find the area of the portion of the cylindrical surface Y = 4 – x² in the first octant that is…

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Q: Q) S = the part of the paraboloid z = 10-x^2-y^2 above z = 1 F = [x^3, xy, z] Find the flux of F…

A: Step:-1 Given that S is part of paraboloid z=10-x2-y2 above z=1 Since, given that z=10-x2-y2 and…

Q: Calculate the integral of f(z,y, 2) = 6z2 + 6y² + 2³ over the curve c(t) = (cost, sin t,t) for 0<t<…

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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: Evaluate JS yz + 4ryds where S is the surface of the solid bounded by 4x+2y+z=84, z=0, y=0 and x=0.…

A: Use the divergence theorem to find the surface integral,…

Q: Find the equation that solves the area of the surface obtained by rotating the curve x = (y² + 2)% ,…

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Q: Suppose S is the surface of revolution obtained by rotating the curve y about the y-axis. = cosx…

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Q: Calculate the integral I = = • (y² + z²) dx + (z² + x²) dy + (x² + y²) dz where I is the…

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Q: Q#5. Evaluate the surface integral ff(x,y,z)dS When f(x, y, z)= 3xyz and is the portion of the plane…

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Q: 4. Evaluate the integral f. x'y°dy – x°y'dx, where C is the square determined by the lines x = 0, y…

A: As per Bartleby's answering policy, we can answer only one question and here we have answered the…

Q: 9. Find the characteristics of the equation hx = bd and determine the integral surface which passes…

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Q: Exâmple '7.21 Evaluate the surface integral / y?2² dS where o is the part of the cone x2 + y? that…

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Q: Evaluate the surface integral + y² + 6z² ) d$ where S is the part of the cone z = 6 - Vx? + y above…

A: Calculate ∫∫Sx2+y2+6z2dS; wherethe surface S is a part of the cone z=6-x2+y2above the z=0 plane.Then…

Q: Find the surface area of the part of the plane 2x+2y +z=4 that lies inside the cylinder x²+y² = 2.…

A: Given that, the equation of the plane is 2x+2y+z=4 and the equation of the cylinder x2+y2=2. Note…

Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x²…

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Q: 3. Evaluate , (x + z)dS where the surface S is the first-octant portion of the cylinder y² + z² = 9…

A: Step:- 1 Since, we know Surface integrals ∫∫Sf(x,y,z)dS=∫∫Df(x,θ) rx×rθ dxdθ…

Q: 6. Evaluate the triple integral 2x2z +2yz dV where S is the solid that lies below paraboloid z = -r?…

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Q: =t°, y = t² 3. Set up an integral to find the surface area generated when the given curve x = where…

A: Given:      x=t3, y=t2 Interval 0≤t≤1   Surface area generated about x-axis is…

Q: Q#5. Evaluate the surface integral When f(x, y, z) = 3xyz and g is the portion of the plane × + 3y +…

A: We have to find Surface integral  f(x,y,z) = 3xyz Plane given is x+3y+5z = 6 in first octant

Q: 2. Evaluate the triple in tegral where E is the y-2x2+2z20nd the plane y= 8. solid bounded by SI…

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Q: Find the area of the surface. The part of the plane  x + 2y + 3z = 1  that lies inside the cylinder…

A: Compute the partial derivative as follows.

Q: Evaluate the line integral | 27x²yzds with respect to s along the curve C : x = t, y = t³, z = ; t(0…

A: The line integral is ∫C27 x2 y z ds x=t, y=t3, z=23t30≤t≤1  dxdt=1, dydt=3t2, dzdt=2t2

Q: The area of the surface obtained by rotating the curve y = 1 I+ X, 1 <xse about the line x = 28 is…

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Q: Calculate the integral of f(x,y,z)=3x2 +3y2 +z4 over the curve c(t)=(cost,sint,t) for 0≤t≤π. ∫c…

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Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 O x - y -…

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Q: yz do where o is the part Calculate the surface integral of the plane z = y + 3 that belongs to the…

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Q: Find the plane tangent to the given surfaces at the specific point f(x, y) = x2 ln(2x+y) in (-1, 3)

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Q: Given a surface 2xy - In (3z- 2) = 10, wherez=f(x, y). Find zx at y =7, z= 1. Leave your answer…

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Q: Q4 (a) Calculate the surface integral: [] (² + (y² + 2yz) dS where o is the first octant of the…

A: To evaluate the surface integral Given plane 2x+y+2z=6

Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

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Q: 17. Find the area of one side of the "winding wall" standing orthogonally on the curve x = y°, 0 < y…

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Q: 11. Integrate G(x, y, z)=x√y² + 4 over the surface cut from the parabolic cylinder y² + 4z = 16 by…

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Q: What is the equation of the plane to the surface z = e3Y sin(3x) +2 at the point P,0, 3) O x- y + ez…

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Q: 2. Find the area of the surface generated by revolving the given curve about the y -axis. (a)…

A: Given b x=y3, 0≤y≤2c x=9-y2, -2≤y≤2

Q: The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3…

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Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: Evaluate the triple integral I = II 3(x2 + y²) dV where D is the region inside the parabolid z = 16…

A: Integration is the process of finding the anti-derivative function of a given function. The area…

Q: XII. $F•d$ where F = (x,y,z²) and S is sphere of radius 2 with center at 0.

A: F→=x,y,z2, surface S is sphere of radius 2 with centre O=0,0,0To find: ∯SF→.dS→

Q: Find the points on the surface xy + yz + zx - x- z =0 where the ant pla

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Q: The area of the surface obtained by rotating the curve y = 1 < x s e about the line x = 24 is O 2n…

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Q: valuate the line integral J xev% ds where C is the line segment from > (1, 1, 1). This yields:

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Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2…

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Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: Evaluate the surface integral. ds Is 3/2 + y3/2), o s xs 1, 0sys 3 0sx < 1, 0 s ys 3 S is the…

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Q: Q.2) Evalute the surface integral Yz ds where o is the part of the plane x + y + z = 1 that lies in…

A: To Evaluate: Surafce Integral ∬σyzdswhere, σ is the part of the plane x+y+z=1, that lies in the…

Q: 3. Find the area of the surface generated by revolving the curve about the given axis: x = g(y) =…

A: ds= sqrt(1+(dx/dy)^2)

Q: Compute the surface area of the cone generated by revolving c(t) = (2t + 2, 6t) about the x-axis for…

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Q: integrate the given function over the given surface. H(x, y, z) = x2√(5 - 4z), over the…

A: Application of integration: We can use cylindrical coordinate to find a parametric equation for the…