Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to (2,4).

Q: Evaluate the line integral / Vxy° +3 dx +6xy" dy, where C any curve joining (1, -1) to (16, 1).

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Q: If C is the line segment from (6, 1) to, (0,0), find the value of the line integral: S(5y i+ x) • dr…

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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: Evaluate the line integral y = x² from (-1, 1) to (1, 1) and the line segment from (1, 1) to (−1,…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) a…

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Q: Evaluate the line integral Lav where C is given by the line y = lnx, 1 ≤ x ≤e. xy ds,

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Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [ (v - x) dx +…

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Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: Compute the line integral -xdy + ydx 2(x-y)2 +4xy where L is the circle (1-x)2 + y2 = 3 with a…

A: We can write the given line integral as ∫L y2x-y2+4xydx+-x2x-y2+4xydy, where L is the circle…

Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We can solve this as follows:

Q: State two other forms for the line integral ∫C F ⋅ n ds given that F = ⟨ƒ, g, h⟩ .

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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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: Evaluate the line integral ∫Cydx+xdy along the curve y=x2 from the point O(0,0) to the point A(1,1)…

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Q: Evaluate the line integral Say dx +z dy, where C is the line segment from (-1, 1, 2) to (2, 3, 1).

A: Evaluate the line integral ydx +zdy where C is the line segment from (-1,1,2) to (2,3,1). Here i…

Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: (a) Verify that the Fundamental Theorem for Line Integrals can be used to evaluate the integral Sc…

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Q: Evaluate the line integral ,F. dr where F = (sin x, –2 cos y, 5xz) and C is the path given %3D by…

A: Integral F.dr = integral F(r(t)).r'(t) dt

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: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dx + 5x2y2 dy

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Q: Evaluate the line integral (cos x + sin y) ds; C is the line segment from (0, 0) to (x, 67).

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

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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: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

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Q: Evaluate the line integral C:y² = 30x from (30,30) to (0,0). NOTE: Enter the exact answer. [-ydr +…

A: line integral

Q: Evaluate the line integral ∫Cx2ds, where C is a the curve given by the equation y=f(x)=lnx, 1≤x≤e.

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A: Line integral will be path independent if vector field whose integral we need  is conservative…

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s ts 1. (y – x) dx +…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We will calculate the given line integral utilizing given information.

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

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Q: | (xy dx + 2y dy)

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Q: |[-y dx + xy dy]

A: See the attachment

Q: Evaluate the line integral ∫Cxdy−ydx along the curve C defined by the equation y=x3 from the origin…

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Q: 6. Use Green's Theorem to evaluate the line integral fc 2xy dx + (x² + y²) dy, if C is the ellipse…

A: Let R be simply connected region with a piecewise  smooth boundary  'C'. If functions 'M' and 'N'…

Q: Evaluate the line integral T, (“+y) dx + 4 ry dy where L is the path, -> r) = (3 t, 2) with 0 <t <1.…

A: We evaluate given integral

Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

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Q: Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0), (5,…

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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 line integral along the path C given by x = 2t, y = 4t, where 0 stsi. (y - x) dx +…

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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: 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: Evaluate the line integral S. xyevz dy, C:x = t,y = t²,z = t³,0 < t s 1.

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. X + dy

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

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Q: Evaluate the line integral along the curve C. S-Tabe − ydx + xdy, C: y² = 3x from (3,3) to (0,0) O O…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) dy

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