Let be the vector field defined as follows in R2 -yi + xj x² + y² Compute the line integral F(x, y) = Fdr where r(t) = sin((cos(2πt)))i + ((1 – t)e¹ +t)j for 0≤t≤1 O A)0 OB)1 OC)2 O D3 OEM

Q: 4y3 (x² + yª + 1)² ’ (x² + yª + 1)² 2r 5. Let F be a vector field on R² defined by Compute the line…

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Q: 4. Is this vector field F(x,y)=(ycos x)ĩ +(sin x+ y)j being the path-independent field? Please show.

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Q: = (4x° – 7y)i + (9y' + 7x – 7)j %3D - ndary of the parallelogram in the following figure (note the…

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A: Given the scalar function φ=xlnz+y-cosx+1. This scalar field is to be evaluated over the path…

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Q: 1. Find the line integral in a vector field a curve consisting of 2 parts. First, the straight line…

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Q: Use the divergence of the vector field to compute F(x, y) = (tan-¹ (2x) fo tan¯¹ (2x) 4 where is the…

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Q: Verify if the vector field F = (x° cos(4y), -x sin(4y)) is conservative and evaluate the line…

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Q: Evaluate the line integral of the vector field (3x2 + 3y + 2xy, 3y2 + 3x + x2) along the curve y = x…

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Q: Consider the line integral cos(x+2y)dx+2cos(x+2y)dy where S is a curve starting at (0,0) and ending…

A: We have to show that F is conservative. When F is given as F=cosx+2yi+2cosx+2yj For the conservative…

Q: where r is the position vector 6. Show that A) - da = | (Ax (Vf)) · da + fA- dl 7. Evaluate the…

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Q: Consider the vector field F(x, Y, z) = 3x?yi+ (x³ + 1) j+9z²k. Let C be the circle cut from the…

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Q: Prove that F(x, y, z) = (y 2 cos x+z 3

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Q: Show that the vector field F(x, y, z) = (-4y cos(4x), 4x sin(–4y), 0) is not a gradient vector field…

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Q: 1. Determine whether F(x, y) et sin yi + e" cos syj is a conservative vector field.

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Q: Show that the vector field F(x, y, z) = (-ycos(8x), 8x sin(-y), 0) is not a gradient vector field by…

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Q: 1. Let F =i+y^2j +z^4k. Find the general flow lines for this vector field. Present the flow line…

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Q: Show the vector field V = (8xy³ z, 12x²y² z, 4x²y³) is irrotational, and find its potential. Then,…

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Q: A vector field is given by F = (2y + 3)i + xz j + ( yz -x)k, evaluate ∫ ?. ?? c

A: Given: F→=(2y+3)i⏞+xzj⏞+(yz-x)k⏞ C is the curve given by r→(t)=2ti⏞+tj⏞+t3k⏞ where t varies from a=0…

Q: vector field in the plane,

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Q: Calculate line integral A from (3,-7, 7) to (0,5,-3). F F. dr of conservative vector field F(x, y,…

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Q: Which vector field F has graph イメ イ* メド 大 と と

A: Given :   Vector field graph is given