Evaluate the line integral, where C is the given curve. ∫CF(x,y,z)⋅dr where F(x,y,z)=xi+yj+ysin(z+1)k and C consists...

Evaluate the line integral, where C is the given curve. ∫_CF(x,y,z)⋅dr where F(x,y,z)=xi+yj+ysin(z+1)k and C consists of the line segment from (2,4,-1) to (1,-1,3).

Expert Solution

milcah answered 2 years ago

Given the line integral ∫c F(r) · dr where F(x, y, z) = [mxy − z3...

Given the line integral ∫c F(r) · dr where F(x, y, z) = [mxy − z3 ,(m − 2)x2 ,(1 − m)xz2 ] (a) Find m such that the line integral is path independent; (b) Find a scalar function f such that F = grad f; (c) Find the work done in moving a particle from A : (1, 2, −3) to B : (1, −4, 2).

Evaluate the line integral, where C is the given curve, where C consists of line segments...

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Evaluate the line integral ∫_C F⋅dr, where F(x,y,z)=−4sin(x)i+3cos(y)j−4xzk and C is given by the vector function...

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Q2. Given the line integral C F (r) · dr where F(x,y,z) = [mxy − z3,(m...

Q2. Given the line integral C F (r) · dr where F(x,y,z) = [mxy − z3,(m − 2)x2,(1 − m)xz2] ∫ (a) Find m such that the line integral is path independent; (b) Find a scalar function f such that F = grad f ; (c) Find the work done in moving a particle from A : (1, 2, −3) to B : (1, −4, 2).

Evaluate the line integral C F · dr, where C is given by the vector function...

Evaluate the line integral C F · dr, where C is given by the vector function r(t). F(x, y, z) = sin(x) i + cos(y) j + xz k r(t) = t5 i − t4 j + t k, 0 ≤ t ≤ 1

Evaluate the line integral ∫CF⋅dr∫CF⋅dr, where F(x,y,z)=sin(x)i+cos(y)j+4xzkF(x,y,z)=sin(x)i+cos(y)j+4xzk and C is given by the vector function r(t)=t3i−t2j+tkr(t)=t3i−t2j+tk...

Evaluate the line integral ∫CF⋅dr∫CF⋅dr, where F(x,y,z)=sin(x)i+cos(y)j+4xzkF(x,y,z)=sin(x)i+cos(y)j+4xzk and C is given by the vector function r(t)=t3i−t2j+tkr(t)=t3i−t2j+tk , 0≤t≤10≤t≤1.

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.

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Evaluate the line integral ∫CF⋅d r where F=〈4sinx,cosy,xz〉 and C is the path given by r(t)=(t^3,3t^2,3t)...

Evaluate the line integral ∫CF⋅d r where F=〈4sinx,cosy,xz〉 and C is the path given by r(t)=(t^3,3t^2,3t) for 0≤t≤1 ∫CF⋅d r=

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