Compute the integral of the vector field F(x, y, z) = (5x, 5y, 2z? ) over r(t) = (cos(t), sin(1). t) for 0 < 1 < a. (Use symbolic notation and fractions where needed.) F. dr =

Q: b) Given the vector field F(x, y, z) = y² tan 2x i - (lnx) (sin z) j+ey k. Find i. div F ii. curl F…

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Q: 5. Consider the vector field F(x,y,z) = yzi + xzj+(xy+2z) k and the curve C given by r(t) = (t+ sin…

A: Given vector field: Fx,y,z=yzi+xzj+xy+2zk Curve C is given by: rt=t+sin12πt,t+cos12πt,2t,   0≤t≤1…

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A: We find the required integrtion using fundamental theorem of line Integral.

Q: OSketch the vector field F(x, y) = -5i – 5j and calculate the line integral of F along the line…

A: Solution:-     Given that, F→ x,y=-5i∧-5j∧we have to calculate the line integral ∴we have to…

Q: Evaluate ∫C F. d r for the vector field F = y i - x j counterclockwise along the unit circle x2 + y2…

A: Evaluate ∫_C F. d r for the vector field F = y i - x j counterclockwisealong the unit circle x2 + y2…

Q: . Consider the vector field F(r, y, 2) = (8r sin y, 4x² cos y – e"z, -e" – sec² z). %3D | F. dR…

A: For a vector field F→, the line integral about the path C is ∫CF→·dr. Let rt be the parametric…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

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Q: Compute the following definite integral of a vector-valued function: Cos t i- tj + te’k ) dt sint +1

A: Please refer the attached image for complete solution.

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: the functions below. F(x, y, z) = x i – zj+ y k r(t) = 5t i + 9t j – t² k (a) Evaluate the line…

A: Consider the given function: F(x,y,z)=xi-zj+yk and C is given by  r(t)=5ti+9tj-t2k   , -1≤t≤1

Q: For the vector field G = (yety + 4 cos(4x + y))i + (xey + cos(4x + y)) 5 I find the line integral of…

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Q: Given the vector field F(x,y)=(y3+4x2-2)i+(3xy2+2y+2)j. Evaluate the line integral to (0,1) along…

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Q: EX2 : Find Divergence and Curl of the field function f j = In (x? + y?)i – 2z -tan + (5z + e' cos…

A: givenf→=ln(x2+y2)i-(2zxtan-1yx)j+(5z3+eycosz)kdefinition of Divergence…

Q: Determine which theorem applies to simplify the following. It is possible that more than one will…

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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: Let W be the region between the sphere of radius 8 and the cube of side 1, both centered at the…

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Q: [F. C F. dr =

A: Given, By the formula to the conservative Vector field F such that

Q: 3. Find the line integral fF.dr where C' is the circle of radius 5 in the xz-plane oriented…

A: The given vector field is .Find the value of line integral  as follows.The parametric surface can be…

Q: dr = wa x b dt r X

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Q: You are given the vector field F(x, y, z) = [3 · x · sin(y · z), cos(2 ⋅ x) ·∙ z, −x · y]. . 1)…

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Q: Evaluate the integral curves for the vector field F(x, y) =i -i .

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