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

Q: Consider the curve segments: 1 - to x = 4 and 3 1 to x = $1: y = x² from x S2: y = Vx from x = = 16.

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Q: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

Q: 3. Find the curvature of the curve given by 7(t) = (t, t², t) nt (-1, 1, –1).

A: Given curve is We know that curvature to given curve at point (-1,1,-1) , that is at t=-1 is

Q: Let C be a smooth curve traced by Ř(t) with R(1) = (2, –1, 1) and R' (1) = (1, –2, –1). Let g(t)…

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Q: Evaluate | f(x,y) ds where Cis the portion of the curve y = In x from the point (1,0) to the point…

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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.

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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: . Find the length of the curve defined by R(t) = (3t+1, 4t3/2, 4-3+2) from the point (1,0, 4) to…

A: Note : The length L of a curve r(t)→=(x(t) , y(t)  ,z(t) )  from t=a  , t=b is given by…

Q: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.

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

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Q: The length of the curve determined by equations x = t² and y = t from t = 0 to t = 4 is %3D %3D %3D…

A: The objective of the question is determine the length of the curve.

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

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Q: 10. If the curves f(x, y) = 0, y, z) = 0 touch, show that at the point of contact, dr dø dr dø dy dx…

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: consider the curve y=x^2-4x+2 show that the normal to the curve at the point x=1 is 2y-x+3=0

A: TO SHOW THE EQUATION OF NORMAL AT x=1 IS  '2y-x+3 =0' GIVEN y = x2-4x+2 EQUATION OF NORMAL AT x=1 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: 10. Let ø(x, y, z) = r*y+ z. Find Sc Vø• dr, where C is any curve starting at (1,0,0) and ending at…

A: we have given φ=x3y+z⇒∇φ=3x2y i+x3j+1kr=xi+yj+zk⇒dr=dxi+dyj+dzk∇φ.dr=3x2ydx+x3dy+dzwhere c is any…

Q: What isfor the curve given by x = (t – 1)³ and y = vt ? | dx 1 2VE 6VE(t-1)2 3(t-1)2 O Option 4…

A: Using chain rule of differentiation

Q: 4 Find the curvature k of the plane curve y = x +- at x = 1. K =

A: Given curve is , y= x + 4x  at x=1

Q: Let C be the curve which is the union of a quarter circle and a line segment. The quarter circle…

A: Consider the given information.

Q: Let C be the curve connecting (0,0,0) to (1,3,1) to (3,4,4) to (2,1,3) to (0,0,0) Evaluate + y)dx +…

A: Given,     and

Q: 1. Find the equations of the normal and osculating planes of the curve x = Int, y = 2t, z = t? at…

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Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: Express the curve by an equation in x and y given x(t) = sin(t) and y(t) = 8 + cos² (t). a) O-x² +y…

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Q: compute the length of the curve over the given interval.  r(t) = (2t2 + 1, 2t2 − 1, t3), 0 ≤ t ≤ 2

A: Length of a curve is also like computing distance between two points but with the restriction that…

Q: Let f(x, y) = x²y – xy. Evaluate | Vf•dr where C is any oriented curve from (4, –1) to (1,5).

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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.

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Q: dz -, n = 2,3, 4, ... where z = a is inside the simple closed curve C. (z – a)" Evaluate

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Q: Find the curvature k of the curve given by r(t) = (2t²,t, ¿ť²)

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

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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

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

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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: 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).

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Q: Let C be the curve connecting (0,0) to (1,2) to (0,6) to (0,0) using straight lines. (5x*y – 3x²y+…

A: Greens theorem based problem......

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

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Q: Evaluate § F · ds, where F = 2x(x+y)i + (x² + xy + y?)j and the positively-oriented curve C encloses…

A: Here we will use greens theorem to find line integral of vector field For a vector field F→= Pi^+Qj^…

Q: Find the length of the curve defined by R(t) = (3t+1, 4t³/2, 4 - 3t²) from the point (1,0, 4) to (4,…

A: Given…

Q: Let a, b > 0. Show that S = {(x, y) E [a, 00) x R| - = 1} is a smooth curve.

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Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

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Q: Find the family of curves orthogonal to the family 4y2 + 3x2 = k when x > 0 and y > 0. (A) 3y2 – 4x2…

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Q: py*(1 + x*)dx + 2ytan xdy ,where C is closed curve xi +yi = 1

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

A: According to the given information, it is required to use green’s theorem to evaluate the integral.