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

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

A:

Q: Evaluate the line integeral F. di where C is the curve given by 7 (t) = tỉ – t3 + 2tk, 0S t < 2 and…

A:

Q: Find T, N, and B for the curve r(t) = (10t, 10t, e') at (0,0, 1).

A: Given: we have ,

Q: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

A:

Q: Evaluate y+z) ds along the curve r(t) = 2ti + tj + (4 – 2t)k, 0sts1.

A:

Q: Let C be the curve given by r(t) = (t cost,t sin t,t).(a) Show that C lies on the cone x 2 + y2 = z2

A: Consider the parametric equation of the curve C : rt=tcos t,t sin t, t. To show C lies on cone…

Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

A:

Q: Compute f ds for the curve specified. f(x, y, z) = 2x2 + 8z, c(t) = (e*, t², t), 0 sts 1

A:

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

A:

Q: Let C be the curve defined by T(t) = (2 + 2 sin(t), 3 – 2 cos(t)) for 0 < t < 4x=²) dx + (2xyev" +…

A: Given the integral is ∫Cy2exy2+4x-2dx+2xyexy2+2dy. Rewrite the integral as ∫CF·→dr→:…

Q: Let C be the curve defined by 7(t) = (2+2 sin(t), 3 – 2 cos(t)) for 0 <t< L (e + 4z) dz + (2zye" +…

A:

Q: Evaluate f ds where C is the given oriented curve r(t)-(cos (t) sin(t) 3t ) for (Osts4n Y and…

A:

Q: Consider the curve C parametrized byx = (t^2+1)/(t^2-1) and y = (2t)/(t^2-1) for all t in (−∞, −1 )…

A: Given:

Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

A:

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: The value of le ydx + zdy + xdz where C is the curve x = y = z = 2t2 from t = 0 to t = 1 is A В 15 C…

A:

Q: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

A:

Q: Use Green's Theorem to evaluate | F. dř, where F = (Va + 4y, 2x + 9) C consists of the arc of the…

A:

Q: Sketch the plane curve r(t) = ti + t2j and find its length over the given interval [0, 4] .

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Use the Midpoint Rule with N = 10, 20, 30, and 50 to approximate the given curve's length. %3D c(t)…

A: We are given the curve :c(t)=(cos t, esint) The length of the curve: s=∫02π-sin t2+(cos t esin t)2…

Q: Let y be the part of the curve y = x² running from (-1,1) to (2,4). Calculate xy dx + (x + y) dy.

A: (1)

Q: 5. Let C be the curve parameterized by r(t) = (t,-t,t²) Evaluate y ds.

A:

Q: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

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: The length of the curve defined parametrically by: x = e'cost, y = eʻsint,0 <t <, is equal to:…

A: given parametric curve x=etcost     y=etsint

Q: Evaluate G(x, y)dx G(x, y)dy and G(x, y)ds on the curve C indicated by = 2t, y = t2, where t is on…

A: If ∫cf(x,y) dx typeof integral is given then the function is integrated with respect to x and…

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: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

A:

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: Can there be a curve satisfying the following conditions? d2y/dx2 is everywhere equal to zero and,…

A: To check: The curve satisfying the given condition or not.Explanation:

Q: |Verify that Green's Theorem is true for S,3(y2 – x) dx + (x² – y)dy given that the curve C is…

A:

Q: Find the length of parametrized curve given by x(t)=12t^2−12t, y(t)=−4t^3+6t^2+9t where t goes…

A: Let us consider the parametrized curve x(t) and y(t)  The length of the curve is obtained as…

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

A:

Q: Determine the torsion at t = 0 of a curve a : [−1, 1] → R3, a(t) = (2t, t^2, t^3/3). Moreover,

A:

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: Use Green's Theorem to evaluate | F. dr, where F = (Va + 5y, 2x + Vỹ ) and C consists of the arc of…

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: A curve in the æy-plane is defined by (x(t), y(t)), where x (t) = t² and y (t) = tª + 1 for t > 0.…

A: Option A is correct answer, Detailed explanation is given below.

Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below

Q: IF=(x+y)i+(y– )j+z?k over the curve r(t) = (t²,t²,t*), 0sts1

A:

Q: let rit)= demti+ dsintf+? Find the length of this curve from t=0 to t = 4.

A: we have to find the length of the curve

Q: If C denotes the curve parametrized by x = t, y = 2t2, z=t°, 0 <t < 1, then fx dz +y dy + z dx C O…

A:

Q: The value of f. ydx + zdy + xdz where C is the curve x = y = z = 2t? from t = 0 to t = 1 is

A: Here we have to find the value of ∫cydx+zdy+xdz where C is the curve x=y=z=2t2 from t=0 to t=1.

Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.

A:

Q: Find the tangent plane to the curve T = [t, t², t³] which pass through point M (2, –, –6) .

A: If the parametric equation of a curve is given by , then the tangent direction is given by . The…

Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

A:

Q: Let C be the part of the curve x? + y² = 1 with y 2 0, oriented counter- clockwise. Evaluate F. dr,…

A:

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