25. Evaluate |F•T ds for the vector field F = x²i – yj along the curve x = y? from (4, 2) to (1,–1).

Q: 5) Consider the conservative force field F(x, y) = (6x²y? + cos(x), 4x y). a) Give a general…

A: For a vector field F=P,Q that is open and simply connected in a region with continuous first order…

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…

Q: (1) Is the vector field F(x, y) = (2æ*y^ + æ) î + (2a*y³ + y) Î conservative? Support your answer…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 5. Find a potential function corresponding to the vector field F(r,y, 2) = (2r, 3y, 4:).

A:

Q: 6. Let F = (x³ sin y, a* cos y). COS (a) Is F a conservative vector field? (b) If your answer to…

A:

Q: Consider the vector field F = (5x + 6y, 6x + 4y). F - dr along the curve C given by r (t) = (t², t*)…

A: ∫CF→·dr→=∫abF(r(t)) r'(t) dr

Q: S. Evaluate F Tds for the vector field F= x2i – yj along the curve x = y² from (4,2) to (1, - 1).…

A:

Q: Q4: Find the curl of the vector field F(x, y.2) = x*/yi +j+ zk at the point(2,4).

A:

Q: 9. Compute the flux of the vector field F(x, y) = (-x sin(1+xy) – 4 cos(TY), y sin(1+ xy) + 6x)…

A:

Q: Q3) Compute the work done by the force field F(x,y,z) = (3x, xz, y) on the curve C, where C is the…

A:

Q: 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

A:

Q: 5. Find the potential function for given vector field: F = (e* In(y))i + + sin(2))j + ycos(z)k

A:

Q: 8. The component of the field F= (1,2,3) normal to the plane z = -3x + 3y -1 is (a) 0. (b) –2//19.…

A: If we are given a plane equation in the form Ax+By+Cz=D, then the normal vector to the plane will…

Q: 3. Find the work done by the force field F(1, y) = y² i+ ryj on a particle moving from (0,0) to…

A:

Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzĵ + xyk in moving from (1,1,1) to…

A: The equation of a line joining by the points and is given as the following.

Q: 10. () The gravitational field F(x) = mMG Ex is a conservative vector field.

A: We shall show that F is conservative vector field by using vector calculus please follow next step…

Q: Compute the line integral of the vector field F = (3zy-¹, 4x, -y) over the path c(t) = (e¹, e¹, t)…

A:

Q: | 23. Find the outward flux of the field F = ( 3xy i + (e* + tan¯ly)j х 1 + y?, across the cardioid…

A:

Q: 3. Use the fact that F = is a conservative vector field to evaluate SF. dr when C is the path r(t)…

A:

Q: Find the work done by the force field F(x,y) = 4yi + 2xj in moving a particle along acirclex^2 + y^2…

A: Step2

Q: 2. Given that F(x, y, z) = (e, xey + e², ye²) is a conservative vector field. a. Find a potential…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 5. Suppose that the vector field F = is conservative. Find a potential function of the vector field…

A:

Q: Find the work done by the field F(x,y, z) = (6z, 12x, y?) along the curve r(t) (cos(t), sin(t),…

A:

Q: Find the work done by the vector field F = ( – 2, – 4y, 2æ) in moving an object along C in the…

A: Let F be a vector field defined on a smooth curve C whose parametric equation is given by rt, a≤t≤b.…

Q: 5. Show that F =(y cos(x),sin(x)+ y) is a conservative vector field and use this to calculate the…

A: Given: F → = y cos(x), sin(x) + y. A vector field F→ = P, Q is said to be conservative if partial…

Q: 2. Given F(x, y) = (4x³y² - 2xy³)i + (2x¹y − 3x²y² + 4y³)j is a - conservative vector field. a. Find…

A: To find the potential function for the given conservative vector field :-

Q: (iv) Find the work done by the force field F(x, y) = x²i+ yeªj on a particle that moves along the…

A:

Q: 2. Letr =√x² + y² + z². (a) For n ≥ 1 and r> 0, express V(r-n) in terms of r and the radial vector…

A: Given  solution(a): Radial vector field  solution(b):

Q: I Need help for this question

A:

Q: 4. Evaluate the line integral Vf-r'dt, where the curve C is given by the vector function r(1)…

A:

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+ e*cos(y))j through the right…

A: Solution

Q: Find the work done by the force field F(x, y) = xi + 2yj on a particle moving along the path C:x =…

A:

Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzj + xyk in moving from || (1,1,1) to…

A: The given question is related with work done. We have to find the work done ∫CF→ . dr  in the force…

Q: Calculate the work done by the field F when the object moves along the given path from the initial…

A:

Q: 9. (~Ch16 Review #13) Find the work done by the conservative vector field F(x, y) = along the curve…

A: given a conservative vector field  Fx,y=4x3y2-2xy3,2x4y-3x2y2+4y3 and a curve  rt=t+sinπt,2t+cosπt…

Q: 19. (a) Evaluate the line integral F. dr, for F(x, y) = ex−¹ i + xy j and C is given by r(t) = t² i…

A: (a)F(x, y) = ex-1 i + xy j   And C: r(t) = t2i +t3j , 0≤t≤1.⇒drdt = 2t i + 3t2j and F(r(t)) = et2-1…

Q: 6. Compute ſ, F-·dr where f(x, y) = (y² cos x, 2y sin r) and C is the straight line path starting at…

A:

Q: 2) Determine the work done by the vector field F along the curve y. F(x, y. =) = (x sin y, 2e*, 2xz)…

A: First I have written about the work done by the given vector field in the direction of the given…

Q: d the work done by the force field F in moving a particle along the curve C. F = xyi + 3j + 9xk; C:x…

A:

Q: 16. Compute the flux V· nds of the vector field V(r, y) = (x² – 2ry, y² – 2xy) across the curve C :…

A: We have to compute the flux ∫ℂV·nds of the vector field Vx,y=x2-2xy,y2-2xy across the curve…

Q: 43 Find the work done by the force field F(x, y) = (x² ln(y + 5), -) on a particle 3(y + 5) that…

A: Given force field F(x,y)=x2ln(y+5),x33(y+5) and circle x2+y2=4. The objective is to find the work…

Q: 2. Find the circulation and flux of the field F(r.y) = (-y,r) along and across the curve 7(1) =…

A: We have to find the circulation and flux of the field F(x,y)= (-y,r) along and across the curve…

Q: (b) A potential function for the vector field F (x, y) = (2x + 1)(x² + x + 1)² 7+ (2y + 1)(y² + y +…

A:

Q: Evaluate the line integral of the vector field F = xy²i+ x²yj along the curve r(t) = (t+sin,t+cos-…

A:

Q: Find the work done by the force field F(x, y) = xyi+ x²j on a ,2 particle that moves along the curve…

A: Consider the given force field Fx,y=xyi+x2j Then, F⇀x,y=xy,y Write in parametric form y=t  then…

Q: 2: Compute the work done by the force field F = (y, -x) to move an object from point A = (1,0) to B…

A:

Q: Evaluate ∫C F . T ds for the vector field F = x2 i - y j along the curve x = y2 from (4, 2) to (1,…

A: Given information: The value of F=x2i+yj, x=y2 and from (4, 2) to (1, -1). Calculation: Consider…

Q: Given vector field F(x, y) = (4x³y? – 2xy³,2x*y – 3x?y² +6y³) and curve C defined by C: 7(t) = (t+…

A: Here we will find out the required value.

Q: ermine whether the vector field F(x, y, z) = (x³, 3zy², y³) is conservative on R³. If so, find a…

A: