Evaluate F.dr by Stoke's Theorem for F = yz i + zx j+ xy k and C is the curve of intersection of x + y? = 1 and y = z?. Ans. 0

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…

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

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Q: Let f (z)=z. Find zp( z) 4} from z =0 to z=4+2 along the curve C given by z =t? +it. (A) -10 - (C)…

A: Use the definition of path integration of analytic function.

Q: 1 - Findthe lenght of the Curve a) r(t)* = (3cost)i³ + (3sint)j* + 4tk¬ for 0 < t < 2n b) r(t)* =…

A: Use formula of length of curve

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A: If r(t) = (f(t) , g(t) , h(t))then L = ∫ab r→'(t)  dtwhere  r→'(t)  = f'(t)2 + g'(t)2 + h'(t)2

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Q: Evaluate S. x?dz + z?dy + y?dx where C is the curve x = t2 ,y = t², z = t² from t = 0 to t = 2.

A: We will use concept of line integral to solve this.

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Q: 13.3. Let y be the curve given by z(t) = t + it?, 0<t < 2T. Evaluate |z|²dz.

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Q: Verify Stokes’s theorem for F = , where C is the curve C: x2+ y2=4 , z = 2.

A: Stoke's theorem problem...

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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…

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Q: Find the exact length of the curve x = t sin t y = t cos t for 0 <t< 1. You may use the following…

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Q: Let C be the curve parameterized as follows F(t) := (9 cos(t), 9 sin(t), 12t), 0<ts 10 and let f(x,…

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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 C be the curve in space given by the following parameterization. r(t) = tỉ + t²j + 9k, 0 < t s…

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Q: Let F = e'i+(xe' -e')j- ye'k and cbe a smooth curve defined by Then the value of the line integral…

A: The formula is  ∫F.dr=∫F(r(t)).r'(t)dt Here…

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

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Q: Practice by Evaluating Fodr where, F(x, y) = e" (sin(y)î + cos(y)ĵ) C: is a smooth curve from (0,0)…

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

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Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

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)…

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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.

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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: c) By using Green's theorem evaluate OUIM GUTM U where C is a closed curve starting from the origin…

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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: Let m be a positive real number and C be the curve given by: r(t) = mcosti – m(sint + 3)j + (5 –…

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Q: The value of [F. dī where F= x?y² i + y j and C is the curve y? = 4x in the XY-plane from (0, 0) to…

A: I am solving this in step 2.

Q: Consider the curve x2/3 + y2/3 =4. Let L be the tangent line to this curve at the point (1 , 3/3),…

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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: Let f(x, y) = 3r + x²y – yx². Evaluate F- dr where F = Vƒ and C is the curve given by r(t) = (2t,…

A: Consider the function  Where   and curve C is given by

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: Consider F and C below. (y?z + 2xz?)i + 2xyzj + (xy? + 2x2z)k, F(x, у, 2) %3D C: x = Vt, y =t + 4, z…

A: we have been given F(x,y,x)=(y2z+2xz2)i+2xyzj+(xy2+2x2z)k we have to find the f such that F=∇f so…

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: x(t) = t°; y(t) = t® is not a parameterization of the ,3. curve y = x Select one: True False

A: By definition, a function is a special case of a relation between the members of two sets. It is a…

Q: Calculate | F.dr, Where F(x. y.z) =(x+yli+(y-+2k. r(t)=i+j+k , 0stsl. is the curve C given by 11 15…

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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: Let C be the curve in space given by the following parameterization. r(t) = tỉ +t²j+t*k,-2sts 1.…

A: The solution is given as

Q: A curve joining the points Pi and P2 in R2 is parameterized by two different paths, 7(t); t1 0.…

A: Given: →γ(t);t1≤t≤t2→(τ);τ1≤τ≤τ2β To find: a) Prove that ∫t1t2→γ'(t)dt=∫τ1τ2→β'(τ)dτ. b)…

Q: 2. If F(x, y, z) = y²i+(2xy+e3=)j+3ye³=k. Evaluate F·Î ds, where C is the curve represented by r(t)…

A: Given F→x,y,z=y2i^+2xy+e3zj^+3ye3zk^ and the curve is C given by r^t=cost,t,sint,  0≤t≤π2. Find…

Q: Suppose a curve C is parameterized using parameter t. Suppose also that y(t) > 0 for te [a, b). Then…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: nclosed between the curves y= r'and x= y? 18 16 14 12 12 14 16 18 -1 -1 O 02 04 0.8 0.6 0.4 0.2 0.6…

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Q: Q 3. For a curve in the x y plane differentiate between dy and dy. Brief and to the point answer is…

A: Query- For a curve in the x y plane differentiate between dy and δy, write the answer briefly,…