Integrate the function H(x,y,z) = 2x2/37 – 12z over the parabolic dome z= 3- 3x - 3y2, z> 0. .... || H(x,y,z) do = S (Type an exact answer, using n as needed.)

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: Evaluate the triple integral. 2xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: Evaluate the line integral f e-*(cos y dx - sin y dy), where c is the rectangle with vertices (0,0),…

A: The line integral function is ∫Ce-xcosydx-sinydy. The vertices of the rectangle is 0, 0, π, 0, π,…

Q: 6. The solid bounded by x = y², and x = 8 – 2z2 – y?.

A: To find the triple integral over the given solid bounded by x=y2,x=8-2z2-y2.

Q: Exercise 10.6 Evaluate the line integral using a method of your choice. e¯*(cos y dx + sin y dy),…

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Q: evaluate both the line integral and the double integral. 16. P(x, y) = 2x – x³y°, Q(x, y) = x³y°, C…

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Q: Find the potential u(x, y) for u +u =0 in the rectangle 0<x< 2 and 0 < y s 2, if the upper side is…

A: The given problem is to solve the potential u(x,y) Laplace partial differential equation, we have to…

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: compute the line integral f(x, y) ds for the given function and path or curve. f(x, y) = x – y, the…

A: Given: fx,y=x-y To Find: Line integral ∫Cfx,yds over the unit semi-circle x2+y2=1, y≥0

Q: 5xy dv, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by…

A: The given integral is ∭E5xydV. The region E lies under the plane z=1+x+y and above the region in the…

Q: Evaluate the triple integral. 16.  ∫∫∫T  xz dV , where T is the solid tetrahedron with vertices…

A: The solid tetrahedron T with vertices 0, 0, 0, (1, 0, 1), (0, 1 ,1) and 0,0, 1. The solid region is…

Q: Evaluate the line integral/ (ax + 2y)dx +x dy, where C consists of the path C from (0,0) to (3,0),…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y+ 18z on the elipse…

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Q: Calculate the double integral (x + y)²ex* - y² dx dy where R is the square with vertices (2, 0), (0,…

A: According to the given information, it is required to find the integral over R where R is square.

Q: Find the absolute maximum of f(z,y) = 4x – 2xy+ 6y-8z+ 2y+3 on the region R= {(x,y)|0 <AA2,-1 < y<…

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Q: Evaluate the line integral (direct method) | (3x– y) dx – x dy , where C consist of the parabola…

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Q: 2. Show that the surface area of the solid of revolution obtained by revolving the curve y = 1/x, x…

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Q: The surface area of the surface generated by revolving y=1-x² for 0<x<1 about the x- axis is s=…

A: If you like the solution then please give it a thumbs up.... The Answer is:              S =…

Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

A: Solution:

Q: Evaluate the triple integral // x dV, where T is the solid tetrahedron with vertices T (0,0, 0),…

A: Here we have to evaluate the triple integral , where T is the solid tetrahedron with vertices…

Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: Evaluate the line integral (direct method) |(3x– y) dx – x dy , where C consist of the parabola y=…

A: Given integral is, ∫C(3x-y)dx-xdy

Q: Evaluate the triple integral ∭E(x+2y)dV where E is bounded by the parabolic cylinder y=2x2 and the…

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Q: 2. Integrate f(x, y) = sin /x2 + y² А. over the closed unit disk.

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Q: Find the potential function for F(x,y,z) = (x^-1z)i + (y^-1z)j + ln(xy)k. Show all steps and explain

A: Potential function of  F, is f such that ∇f=F.

Q: How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the…

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Q: (7) Determine the upward flux of ▼ × F through the part of the elliptical cone C = {(x, y, z)|z = 2…

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Q: Use Green's Theorem to evaluate the line integral. y dx + 7x dy C: square with vertices (0, 0), (0,…

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Q: 8) Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = y - y?…

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Q: Evaluate the triple integral. SSLĘ 8x dV x = 2y2 + 2z2 and the plane x = 2. where E is bounded by…

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Q: The surface area of the surface generated by revolving y= 1-x2 for 0<x<1 about the x - axis is S = […

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Q: Consider the function f (x,y) = x3y3 + xty. Show that it is homogeneous of %3D degree 5 and verify :…

A: A function f(x, y) is said to be a homogeneous function if f(λx, λy)=λnf(x, y) where λ is a constant…

Q: No. Date Evaluate fff dv G x² + y² where G is a solid that lies inside cylinder *+(4-2)² =4 obove…

A: we will use cylindrical co ordinate system to solve the given integral

Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 7y2 + 7z² and the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the…

A: The objective is to evaluate the triple integral ∫∫∫E8xdV, where E is bounded by the paraboloid…

Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0

A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.

Q: Integrate f(x.y) = /16 - x over the smaller sector cut from the disk x2 + y2 s 16 by the rays 0= and…

A: In the question we have to evaluate the value of integral.

Q: Use the Fundamental Theorem of Line Integrals to find the exact value of the path-independent line…

A: First of all hare we check for the path independent line integral then solve for moving over the…

Q: The line integral (x+/y) ds , where C is the line segment joining the points (0, 0) and (1, 1) , can…

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Q: Calculate the double integral. sec) da, R={cx, v) 1 0 s*s2,0s ys} sec2(y) dA, R = = {(x, y) | 0 < x…

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Q: The solid bounded by the surfaces S : -2(: – 2) = y² S2 : 1 = 5– 2y S3: r=0 S4 : y = 0 Ss : z = 0…

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Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

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Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the…

A: here, E is bounded by the paraboloid  x=7y2+7z2  and the plane x=7.    so , at    x=7 ,     y2+ z2…

Q: 3 Find the bounded Solution of : = xt メ>。,t>。 >y(メノ) where y cx, o) = %3D and y co,t) = 0 . Ansi] y=…

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Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and the…

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Q: Find a cubic approximation of r(θ) = (θ 2 , eθ , θ) at θ = 0.

A: given rθ=θ2,eθ,θ to find - cubic approximation at θ=0

Q: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? +…

A: The given line integral is, I=∮y4x2+y2dx+x2x2+3y2dy We know the Green's theorem:…

Q: The volume of the solid generated by the curve y = e¯ª, between x = 2 and x = 7 about the x – axis…

A: Given curve, y=e-x x=2  and   x=7

Q: Find the absolute maximum and minimum Of the function f(x, y) = x + Y on the elliptic region {(x, y)…

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