Use Green's Theorem to evaluate the line integral , 6y² dx + 5x² dy, where Cis the boundary of the square -1

Q: Evaluate the integral |(2e' – 2x) dy +(2xy +1) dx using Green's theorem where C is C 64 ans:-- 3…

A: Using Greens theorem the integral over a closed path can be converted into a corresponding surface…

Q: Evaluate the line integral 2'y dx +a/y² +1 dy for C : r(t) = (VE, t?),0 < t < 1 and then repeat with…

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Q: Use Green's Theorem to evaluate the line integral. cx2 - y?) dx + 5y? dy C: x² + y² = 9 (x² .

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Q: Evaluate the line integral, where C is the given curve. | (x/y) ds, C: x = t3, y = t4, 1sts 2

A: Given: I=∫C(xy)dsC: x=t3  and  y=t40≤t≤2

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤t≤ 1. √(x + 3y²) dy…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s ts 1. %3D (y – x) dx…

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Q: Evaluate the line integral. y dx - x dy, parabola y = x² for 0 < x < 8

A: Given:

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) a…

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Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. (y - x) dx +…

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Q: Evaluate the line integral along the curve C. (xz+2) ds, C is the curve r(t) = (-6-2t) i + tj- 2tk,…

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Q: aluate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

A: Solve integral by changing in terms of t

Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

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Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

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Q: The value of the line integral S(2xy dx + 2x?ydy + dz) C along a path joining the origin and the…

A: We have to find the value of given line integral.

Q: Evaluate the line integral along the curve C. (xz + y) ds, C is the curve r(t) = (-4 - t) i + 2t j -…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. √(²x- (y - x)…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We can solve this as follows:

Q: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

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Q: Evaluate the line integral, where C is the given curve. | 22 dx + x2 dy + y² dz, C is the line…

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Q: Evaluate the line integral S, y ds where C:x = t²,y= 2t, 0 <t < 3

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Q: Verify the Green's theorem for integral x²y dx + xy dy, where C is the boundary described…

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Q: Evaluate the line integral, where C is the given curve. (x + 5y) dx + x2 dy y (5, 1) (6, 0)

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [(x + 3x²) dy

A: To evaluate: ∫C(x+3y2)dy...(1) where C is given by x=2t, y=4t⇒dy=4dt and 0≤t≤1

Q: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

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Q: Consider the integral 16–z² x? dz dy dx x²+y²

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Q: In whatever way you see fit, evaluate the line integral L(10xy-3y+21x dx+ (15xy=+6xyz*)dy+ (15xy='…

A: given line integral ∫c10xy3z3+3y2z3+21x2z2dx+15x2y2z3+6xyz3dy+15x2y3z2+9xy2z2+14x3zdz   ...i…

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s ts 1. (y – x) dx +…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We will calculate the given line integral utilizing given information.

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. y10 dx + x6…

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Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.

Q: B)evaluate the line integral: $5xy'dx- dx +x'ydy where c: y = x; y= x

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Q: Evaluate the integral. V16-a? 1 dy dx dz = -V16-x2 (x2 + y?)1/2 -4.

A: We can solve as follows

Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: Evaluate the line integral f. 4y dx + z² dy + (16 – x²) dz over the quarter of the circle of radius…

A: To Determine: Evaluate the line integral over the quarter of the circle of radius 4 in the xz-plane…

Q: Evaluate the line integral. 15y dx + 14z dy + x dz, r(1) = (2 +r,2.?) for 0 <i<1 (Give an exact…

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Q: Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0), (5,…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 stsi. (y - x) dx +…

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Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t3, t2) for 0 <t< 3

A: Here, x=2+t-1 y=t3 z=t2

Q: Evaluate the line integral. L(4x – 8y) ds C:x + y = 100 (4x - 8y) ds = i |

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Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t³, t2) for 0 <ts 3

A: Given: From the above function, the following can be written,

Q: Evaluate the line integral S. xyevz dy, C:x = t,y = t²,z = t³,0 < t s 1.

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Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: Q#03(a): Use Green's theorem to evaluate the line integral f. (x – 3y) dx (4x + y) dy, where C is…

A: Green's theorem

Q: Evaluate the line integral ſ. 3(x – y) ds along the path C:r(t) = ti + (2 - t)j, 0<t<1

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Q: Evaluate line integral F. dr, where F(x, y) =(2xy)i + (x²+3)j, and C is the path given by r(t) = t =…

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Q: Use Green's Theorem to evaluate the line integral. e cos(2y) dx - 2e* sin(2y) dy C: x2 + y? = a?

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) dy

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