1. Evaluate fL, 2 dv where E lies below the plane z = 2+ 3x + 4y and above the region in the xy-plane bounded by the curves y = x³, x = 1, y = 0

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: Evaluate the triple integral. 3xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

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Q: Transform the equation rydx – (z+2) dy = 0 into the form of a %3D variable separable f(z) dz + g(y)…

A: Here, the given differntial equation is: xy dx-(x+2)dy=0...(1) To write the eqaution in form of f(x)…

Q: 1. Compute  E yz dV , where E is the region above z  0, below z  y, and inside x 2 y 2  4

A: Obtain the limit of integration as follows.

Q: #6. Evaluate the line integral (y dx +z dy +x dz), where C is given by x = Vt, y = t, z = t? with…

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Q: 5. D is the region in the xy-plane bounded by the curves x = cos(y), 3y 27Tx, Зу 3 — 2тх. Evaluate x…

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Q: . 3. Compute E y 2 z 2 dV , where E is the region bounded by x  1
y 2
z 2 and x 

A: The given curves are

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∭E xy dV where E is the solid tetrahedon with vertices…

A: Given Data : Triple Integral ∬∫ExydV and E is the solid tetrahedron with vertices 0,0,0,…

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

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Q: e dV where E is bounded by the parabolic cylinder z = 1 -y and the planes Evaluate the triple…

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Q: Evaluate SS x² y4 dx dy D 1 where D is the region bounded by the hyperbolas xy-2, xyalk parabolas y²…

A: We have to Evaluate the integral  ∬Dx2y-4dxdy where D is the region bounded by the hyperbolas xy=2,…

Q: 1. Find the region in the xy-plane in which the following equation is hyperbolic: [(x-y) -1]u +2uy…

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = E : 6y² + 6z²…

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Q: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

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Q: • SSS ²³² x² + y² = 2, and the xy plane. Evaluate e² dV where E is enclosed by the paraboloid z = 6…

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Q: Evaluate xy dV where E is bounded by the parabolic cylinders y = x², x = y² E and the planes z = 0…

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Q: Evaluate ∫∫∫E √x2 + z2dV, where E is the region bounded by the paraboloid y = x2 + z2 and the plane…

A: Given, y=x2+z2 ⇒z2=y-x2z=±y-x2 Therefore the limit of z is -y-x2≤z≤y-x2 On drawing the graph in the…

Q: (1) Sketch the regions of integration. (a) 3m/2 (b) (r,0)r drdo 3m/4

A: The integrations  (a). ∫-π2π2∫04f(r,θ)rdrdθ(b). ∫3π43π2∫34f(r,θ)rdrdθ We have to sketch the regions…

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

A: triple integral

Q: Evaluate the line integral Scy dx + x dy where C is the parameterized path x = t°, y = t³, 1 < t< 3.…

A: follow next step

Q: Evaluate the line integral cy dx + x dy where C is the parameterized path x = y = t° , 2<t< 6. Scydx…

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Q: 4. Evaluate fl, cos (2) dA where D is the region bounded by D = {(x, y)/ vLT <x < V3Ln,0 <y< x² }.

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

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Q: 6- Evaluate the line integral fF dr, where F = [xy, yz, xz] and C is the boundary of the hemisphere…

A: the line integral f F dr, where F = [ry, yz, xz] and C is the boundary of the hemisphere x² + y² +…

Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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Q: 1 Evaluate the double integral| dx dy where T is the quadrilateral bounded by the lines x = 1, x =…

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Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

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Q: 6. Evaluate the triple integral ry dV where E is bounded by the parabolic cylinders y = x² and r =…

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Q: Evaluate 7x dV where E is the region that lies inside the cylinder x2 + y² = 8 E and between the…

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Q: If C is any sectionally smooth curve, which of the following line integrals is NOT path-independent?…

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Q: 4. Evaluate x² dV G where G is a solid that lies in the first octant bounded by x2 + y? = 3z and z =…

A: We have solid G in the first quadrant bounded by x2+y2=3z and z=3 equating the above two equations…

Q: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

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Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. I (a) √(x…

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Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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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: 1 Integrate the function f (x, y) = over the region bounded by r-axis, line æ = 7, and the curve y =…

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Q: where E is the region bounded by the paraboloid y= r+ z2 (Figure 15.4. %3D y = x2 + z?

A: Please rate and feel free to ask any query about any part of the question .

Q: 3.4.6 Evaluate the line integral I = =f( (xy dx + x dy) C where C is the closed curve consisting of…

A: We have to solve the given problem

Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

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Q: Use Green's Theorem to evaluate (e" + y²) dx+ (e" +x²) dy where C is the boundary of the region…

A: we have to evaluate the following by using greens theorem

Q: If C is any sectionally smooth curve, which of the following line integrals is NOT path-independent?…

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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: Set up the triple integral 8y dV, where E is bounded by the coordinate planes and the plane x + y +…

A: To Set up the triple integral for 8y dV, where E is bounded by the coordinate planes and the plane x…

Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

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