Evaluate |F. dR, where F(x,y, z) = (x, – 2, y) and C' is the curve given by R(t) = (2t, 3t, –t2), 0

Q: Evaluate Se (5xy + x² + y²) dx + (x² - y)dy by using Green's theorem, where C is a closed curve that…

A:

Q: Let F(x,y,z) = (z2,x,y}, and let C be the curve that is given by r(t) = (3 + 5t2,3 - t2,t} for 0 ≤ t…

A: Given: F(x,y,z)=z2,x,y and rt=3+5t2, 3-t2, t for 0≤t≤2

Q: Compute F. dr for the oriented curve specified. Jc F(x, y) = (6, y), quarter circle x2 + y? = 1 with…

A:

Q: Let r(t) = E (3t — 3, 5е", — 5е"). Find the line (L) tangent tor(t) at t = - 1. - L: (x, y, z) +t

A:

Q: B) Evaluate the line integral F-dr, where F (x, y) = r*y°i+x²y°j and C is the curve r (t) = (t³ +…

A:

Q: Use Green's theorem to evaluate , (5xy + x2 + y?) dx + (x²-y)dy where C is a closed curve that is…

A:

Q: Compute F• dr for the oriented curve specified. F(x, y) = (9, y), quarter circle x² + y2 = 1 with x…

A: Given:

Q: Evaluate f. x'dz +z?dy +y?dx where C is the curve x = t ,y = t2, z = t? from t = 0 to t = 2.

A:

Q: Verify that Green's Theorem is true for S,3(y? – x) dx + (x2 - y)dy given that the curve C is formed…

A: We have to solve the given integral by Green's theorem.…

Q: find the work done by F in moving a particle once counterclockwise around the given curve. F = (4x -…

A:

Q: Evaluate | F. dR, where F(x, y, z) = (x, –2, y) and C is the curve Ř(t) = (2t, 3t, –t²), 0 <t < 2.

A:

Q: A possible way for the parameterization of the curve C corresponds to: (9t – t² A) r(t) = , t, z(t)…

A: In the three dimensional system, a parameter(usually "t") is used to describe the variables x, y and…

Q: Evaluate F dr where F(x, y, z)=(x, xy, yz) and C is the curve r (t) = (t, t

A:

Q: 2. Prove that the following curves are intersecting with a right angle: 5y-2x+ y –x*y =0 2y+5x+x*…

A: Given curves are  5y-2x+y2-x2y=0and2y+5x+x4-x3y2=0

Q: Let F(x, y) = (3x, 2y) and let y(t) be the integral curve of F passing through the point (x, y) =…

A: Given: F(x,y)=3x,2y andγ(t) be the integral curve of F passing through the pointx,y=8,5 at t=0. To…

Q: Find the work done by F = - 2zi + 7xj + 5yk over the curve C in the direction of increasing t. C:…

A: Solution of this question is

Q: Compute f ds for the curve specified. f(x, y, z) = xz, r(t) = (3e, 2v5t, 4e) for 0sts 1

A: Here the provided function f(x, y, z) of three variable and a curve C is defined. Then the line…

Q: If C is a piecewise smooth curve from (1,2, 3) to (4,5,6), then | . dx + 2 dy + 3 dz=

A: The value of the given function can be found with the help of the integration. Substitution of…

Q: B) Evaluate the line integral F-dr. where F (x, y) = x*y²i+x²y°j and C is the curve r (t) = (t³ +…

A:

Q: Find the work done by F in moving a particle once counterclockwise around the given curve. F= (4x-…

A:

Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

A:

Q: Find the work done by F = xyi+yj - yzk over the curve r(t) = ti + t²j + tk, 0≤t≤1

A:

Q: 6. (a) Show that F = (3a²y+2, x3 + 3) is conservative. (b) Evaluate Sc(3x²y +2)dx + (x³ + 3)dy where…

A: According to the problem, we have

Q: Consider F and C below. F(x, y, z) = (y²z + 2XZ² ) Î + (2xyz)j + (xy² + 2x² Z) K₂ C² X=√E, y = t +…

A:

Q: Find T, N, and k for the space curve r(t) = - ti - (a cosh (t/a))j, a > 0.

A: Unit Tangent. Unit Normal. Curvature.

Q: Evaluate F ds (or F ds) where Jc F = (y – x2, z - y², x – z) and C is the curve r = joining (0,0,0)…

A:

Q: Compute f ds for the curve specified. f(x, y, z) = 2x? + 40z, c(t) = (5e", 5t2, 5t), 0sts 1 %3D

A: Use parametric to solve

Q: 1. Let y be the part of the curve y =r² running from (-1,1) to (2,4). Calculate ry dr + (x+ y) dy.

A:

Q: Use Green's theorem to evaluate S, (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: Since you have posted multiple questions according to company policy we are supposed to be answer…

Q: Evaluate [ f (x,y,z) ds given that f(x,y,z) =, and the curve C is ř(t) = 2ti +t²j+÷tk (1<t<∞) %3D…

A: Given: f(x,y,z)=x2xy+6yz r→(t)=2t i→+t2 j→+13t3 k→   1≤t&lt;∞

Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

A:

Q: 2. Let F(x,y) = (cos(x – 2y), –2 cos(x – 2y)). Find curves C and C2 so | that, F. dr = 0 F. dr = 1

A:

Q: Compute / f ds over the curve specified. (1) f(x, y, z) = z², r(t) = for 0 < t < 2

A:

Q: Compute f ds for the curve specified. f(x, y, z) = z2, r(t) = (2t, 3t, 4t) for 0 sts 2

A:

Q: Let C: [o,2]> R be a curve defined by C(t) = (t²,t'). Evaluate. Sy dx x dy.

A: Given:  C: [0, 2]→ℝ2   is a curve defined by                C(t)=(t2, t3)implies x=t2 and…

Q: 13. Let F (x, y) = (1(²y²)x, af(x²y? , a(y²) Y) and suppose that C is a smooth curve parametrized…

A:

Q: Evaluate f, x*dz + z*dy + y*dx where C is the curve x = t,y = t, z = t? from t= 0 to t= 2.

A: x = t2 ,  y=t2, z=t2 dx = 2t dt,  dy= 2t dt, dz = 2t dt  Putting values in the integral: ∫02t4(2t…

Q: Compute f ds for the curve specified. f(x, y, z) = x²z, r(t) = (3e*, 2/6t, 4e-t) for 0 sts1

A: Given:

Q: Let f(x, y) = x² + y? and C be the curve along y = x² from (0, 0) to (1, 1).

A:

Q: B) Evaluate the line integral F-dr, where F (x, y) = x²y³i+ x°y°j and C is the curve r (t) = (t³ –…

A:

Q: Let a curve be parameterized by x = t³ – 9t, y =t+3 for 1< t< 2. Set up (but do not evaluate) the…

A:

Q: Use Green's theorem to evaluate S,(5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: If L is the tangent line to the curve 7 (t)= (2t-1, t, t-2) at (3, 4, 2) and the point where L…

A:

Q: Show that the curve r(t) = ( t3 /4 - 2)i +(4/t-3)j+cos(t-2)k is tangent to the surface x3 + y3 + z3…

A:

Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

A:

Q: Ext find the anen of the ragion bounded on the leftby the Curve yx, on the right by the line y and…

A:

Q: Find the equation of the tangent plane to the surface z = 3 e^(x−y) at the point (4, 4, 3)

A: We find the equation of the tangent plane to the surface z = 3ex-y at the point (4, 4, 3).

Q: (1) Find the curl of the curve F=(x*y.y*z.2x) (0.0. y+1) (-x'.2'.y+1) b) d)

A: We have to find the curl of the curve F=(x2y,y2z,z2x) curl is defined as the cross product of ∇ with…

Q: Let C2 be the curve defined by R(t) = (t² + t + 3, 4t – 5,2 +t – t²), t e [0, 1]. Evaluate | (x + y+…

A: The solution is given as