2. Evaluate F. dr for F = (-y, x2, 23), where C is curve of the intersection, oriented counterclockwise, of the circular cylinder r² + y? = 4 and the plane x+ z = 3. Sketch the solid and the region of integration

Q: Use cylindrical coordinates to evaluate the triple integral ||| E is the solid bounded by the…

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Q: 5. (a) Evaluate the surface integral /3² dS where o is part of the cone z = VT + y² that lies…

A: As you post multiple questions According to the guideline I only solve the first problem please post…

Q: Calculate the integral f, (3y – 3x²) dæ + (9x) dy where y= aD is the counter-clockwise boundary of…

A: we are allow to solve one question at a time thank you

Q: 7. Evaluate the line integral f, F· dr where F(x,y, z) = x³i – y²j+ zk and C is the x2 + 2xy + y²…

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Q: Evaluate the triple integral. I/| (x - y) dv, where E is enclosed by the surfaces z = x2 - 1, z = 1…

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Q: The volume of the solid generated by the curve y = e, between z = 2 and z = 6 about the z- azis is

A: Given: The curve is y=e-x   To determine: The volume of the solid generated by the curve y=e-x…

Q: Verify Green's theorem in the plane for f (32 - Sy*)dz + (4y – 6zy)dy, where C is the boundary of…

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Q: Evaluate the surface integral I F. dS when F(x, y, 2) = y²i+ 3x² j and S is the graph of - ža (1+æ²…

A: Here, Fx,y,z=y2i+3x2jz=121+x2-y2

Q: Evaluate /// 203 dV G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Here we have to find range of values for x,y and z and then find triple integral

Q: Evaluate the integral f. x'y°dy – x³y'dx, where C is the square determined by the lines x = 0, y =…

A: We have to evaluate the given integral.

Q: Use cylindrical coordinates to evaluate the triple integral □ لاا √² + y²dV, where E is the solid…

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Q: |Use cylindrical coordinates to evaluate the triple integral |/L Vz? + y² dV, E is the solid bounded…

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Q: Calculate ff F.n dS where F x'yzi + 2xj + y?k in the solid region S bounded by the parabolic tube z…

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Q: 4. Let S be the portion of the paraboloid z = 4 – x² – y? in the first octant. (a) Evaluate the…

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Q: Evaluate the triple integral ||//. z°e" dV where E is bounded by the parabolic cylinder z = 16 – y?…

A: The volume of a solid can be calculated using the triple integrals. The unit dV can be written as…

Q: Evaluate the triple integral. [l ydV where G is the solid enclosed by the plane z = y, the xy-plane,…

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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: 3 Use polar coordinates to evaluate the integral (3) f[/x² +y° dA Ris bounded by the semicircle y =…

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Q: Q11// If F = 3xi + 2j – k , Evaluate , F dv where V is region %3D bounded by the plane y=D0,z30,…

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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: Use cylindrical coordinates to evaluate the triple integral |||| Væ² +y² dV, where E is the solid…

A: Mentioned below is the answer

Q: Evaluate the triple integral z dV, where is E bounded by the paraboloid x= 4y+4z2 and the plane x =…

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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: 8. Use Green's Theorem to calculate f, x?y³dx + (xy - y?)dy where C is the boundary of the region…

A: The given integral is ∫Cx2y3dx+xy-y2dy, where C is the boundary of the region lying between the…

Q: The area of the surface obtained by revolving the curve y = yx , for 1<x<4, about the y-axis, is…

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

Q: . Let R be the solid enclosed by the surfaces z = 3r +y and z 8- a2-y?. Fill in the missing limits…

A: According to given graph ∫∫R∫ fx,y,z=∫□□∫□□∫□□  fx,y,z dz dy dx         Z=3x2+y2   to  Z=8-x2-y2…

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: FD is the region in the first octant between the spheres x2+y2+z²=1 and x2+y2+z²=16, then dV =

A: Converting into spherical coordinates

Q: Evaluate the triple integral a dV where E is the solid bounded by the paraboloid a = 10y² + 102² and…

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Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: Evaluate the triple integral z dV, where is E bounded by the paraboloid x= 4y+4z2 and the plane x=…

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Q: Use Green's Theorem to evaluate |(e* +y²) dr + (+r²) dy where C is the boundary of the region…

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Q: 1. Find the surface area of the cone z = Jx2 + y2 that lies between the plane y = x and the cylinder…

A: Surface area in xy-plane

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: Use Stoke's Theorem to evaluate the line integral / 7ydx + 3zdy + dz where C is the intersection of…

A: Use Stoke's Theorem to evaluate the line integral ∫C7y dx+3z dy+ dz, where C is the intersection of…

Q: Evaluate the triple integral /// IdV where E is the solid bounded by the paraboloidz 7y +7 and z=7.

A: To find the triple integral

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: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

Q: Calculate F. dS where F = (3xy°, xe", zª) S is the surface of the solid bounded by the cylinder y? +…

A: Let's find.

Q: Let R:x²<ys 3 be the closed region having boundary C with counter-clockwise orientation. F=[X…

A: We are given that the closed region R: x2 ≤ y ≤ x/3, is having boundary C with counter-clockwise…

Q: E is the region behind the surface y = 4 – x² that is in front of the region in the xy-plane bounded…

A: Given integral: ∫∬E18x dV Given that E is the region behind the surface y=4-x2 that is in front of…

Q: ) Let W1 be the solid half-cone bounded by z = Vx2 + y2, z = 4 and the yz-plane with x > 0, and let…

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Q: Evaluate the triple integral. 5xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A: The point of intersection of the cylinder x=y2 and y=x2 is 0 and 1.

Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

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Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

A: Given problem:- Evaluate the ∫∫∫E z dV, where E is bounded by the cylinder y2+z2=4 and the planes z…

Q: Evaluate the line integral F dr, where C is given by r(t) = (t², t, vT), 0<ts2 and (x, y, z) = (z,…

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Q: Use Green's Theorem to evaluate the line integral (y +eva) dx + (2x + cos y²) dy , where x2 and C is…

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Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

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Q: Use cylindrical coordinates to evaluate the triple integral x² + y dV, where E is the solid bounded…

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