Find the line integral of z2 dx + y dy + 4y dz, where C consists of two parts, C, and C,. C, is the intersection of cylinder x2 + y2 = 16 and plane z = 3 from (0, 4, 3) to (-4, 0, 3). C, is a line segment from (-4, 0, 3) to (0, 1, 5). (Round your answer to two decimal places.)

Q: Please solve the line integral Se F · dĩ In where: F = y²i+2r(y+1)j Is along 2 unique paths from the…

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Q: Evaluate the triple integral. 5x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: From the given  problem:   ∫∫∫E5xdV   We can also write as:…

Q: Evaluate the double line integral S  of the fuinction (x − 2y + z) dS. S: z = 9 − x,  0 ≤ x ≤ 9,  0…

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Q: Use Green’s Theorem to evaluate the line integral  (x^2 − 2xy) dx + (x^2 y + 3) dy where C is the…

A: The given problem is to evaluate the given integral in the contour using the green's theorem in the…

Q: Evaluate the line integral fo(y+z) ds along the curve C defined by the straight-line segment 2 0, y…

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Q: Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C:…

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Q: Find the line integrals of F = 4yi + xj + zk from (0,0,0) to (1,1,1) over each of the following…

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Q: Evaluate the line integral, where Cis the given space curve. xevz ds, C is the line segment from (0,…

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Q: Find the line integral of F = (6x - 6x) i+ 6z j+k from (0,0,0) to (1,1,1) over each of the following…

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Q: Use Green's Theorem to evaluate the line integral: f. In(1 + y) dr – #, dy where C is triangle with…

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Q: Find the value of the line integral of the function f (x, y, z) = x + y + z along the segment AB,…

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Q: Find the integral of f (x, y, z) = 6 z z + 3 over the region inside the cylinder 9 and between -* -…

A: The objective is to find the integral of fx,y,z=6xz+3 over the region inside the cylinder x2+y2=9…

Q: Evaluate the triple integral edV where E is bounded by the parabolic cylinder z = 1 - y² and the…

A: Given ∭x8ey dV

Q: Q:4) Use Green theorem and evaluate the line integral ${Mdx + Ndy} Where M(x,y)=y², N(x,y)=x², C is…

A: See the details solution in below

Q: If  V(x,y)=(8⋅y+5)i+(9⋅x+1)j, dl=dx i+dy j and C is a path which encloses area A,  then the line…

A: We find the line integral  ∮CV⋅dl  Given that   V(x,y)=(8⋅y+5)i+(9⋅x+1)j,  dl=dx i+dy j and C is a…

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

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Q: Evaluate the triple integral. xyz dV, where G is the solid in the first octant that is bounded by…

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Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: We have a paraboloid, and each cross section is a circle, parallel to the plane x = 5. We use…

Q: Choose five other iterated integrals that are equal to the given iterated integral. '8 8 f(x, у, 2)…

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Q: 5. Set up an iterated triple integral in the order dxdzdy that gives the volume of the solid in the…

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Q: Solve for the area of the portion of the cylinder x = /1 – y², which lies between the planes z = 0…

A: Here is the solution of the given problem:  By using line integral to find the surface area of…

Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y? + 5z2 and the…

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Q: Let g(x, y, z) =x- Let S the solid bounded by the surfaces 6y2 + 6z2 and x =6: X = Consider the…

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Q: Evaluate the triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

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: Use the transformation u = - -6x +y, to evaluate the integral [ ( (5x • y) dx dy, where R is the…

A: use the transform u=-6x+y, v=5x+ywe evaluate ∫∫R 5x+y dx dywhere R is the parallelogram bounded by…

Q: Find the line integral of F = 2√√zi-4xj + 3√yk, from (0,0,0) to (1,1,1) over each of the following…

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Q: 2. Evaluate the triple integral where E is the solid bounded by y = 2x² + 2z² and the plane y = 8.

A: A detailed solution is given below.

Q: Let C₁ be a straight line in the Argand plane from (0, 0) to (3, 3), and let C₂ be the path…

A: We have to calculate the following integrals i∫C1z2dz  and ii∫C2z2dz where C1 and C2 are given…

Q: 6. Use a triple integral to find the volume of a solid enclosed by the elliptic paraboloids z = 2x²…

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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: Find the line integral of F= 2√zi-4xj + 3√√yk, from (0,0,0) to (1,1,1) over each of the following…

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Q: |Evaluate the line integral: f.(r² + y) dx + (4x – cos(y)) dy where C is the boundary of the square…

A: According to Greens theorem, the line integral ∮CPdx+Qdy=∬DQx-PydA. BY the extended version of…

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 solid bounded by z = x, z = 2 – x², z + y = 3, and y = 0

A: Volume of a solid is obtained using triple integration by the formulae =∫∫∫dx dy dz The solid is…

Q: Evaluate the line integral (y + z) ds along the curve C defined by the straight-line segment æ = 0,…

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Q: Calculate the (x - 3y)dA R integral by making x=2u+v and y=u+2v conversions, including the…

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Q: Evaluate the line integral In(x + y) ds, z + 2 where C is the line segment from the point (1,0, –1)…

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Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: Evaluate the line integral using the Fundamental Theorem of Line Integrals. (3y dx + 3x dy), where C…

A: Given line integral is: I=∫c3ydx+3xdy It can be rewritten as: I=3∫cydx+xdy                ....(1) As…

Q: Evaluate the triple integral. III. 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the…

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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: 4. Set up an iterated double integral equal to the volume of the solid in the first octant bounded…

A: The region is

Q: Prove that (x,y,z)=(2.25,-1.35,0.169) minimizes 1.5 the integral , [w3 – (xt² + yt – z)]² dw

A: We will use basic knowledge of multivariate calculus to solve this question. Note that we are…

Q: Express by repeated integrals, the volume of the solid bounded above by the plane 2r + 2y - :+1=0,…

A: We are asked to express by repeated integrals , the volume of the solid bounded above by the plane…

Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

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Q: Evaluate the triple integral. 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x…

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Q: Evaluate the line integral, where C is the given curve. (x + yz) dx + 2x dy + xyz dz,  C consists of…

A: C consist line from A (3, 0, 1) to B(4, 4, 1).The equation of the line AB: