If  V(x,y)=(8⋅y+5)i+(9⋅x+1)j, dl=dx i+dy j and C is a path which encloses area A,  then the line integral  ∮CV⋅dl can be evaluated as:

Q: Find the line integral of x ds over C where c is the line segment from (1,0) to (0,1) using two…

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Q: af 11. Suppose + = 0, prove that the line integral | F. fe -dx + ду dr = -dy is inde- pendent of…

A: Here F = fy i+fxj

Q: Calculate the line integral f -y²dx + xdy where ŕ is the path y² = 2x − x² such that x>1 and y > 0.

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Q: 2. Evaluate the given line integral, | (-y,x – y) · dR, where C is the line segment from (1,0) to…

A: To find the line integral we use the equation of line segment in parametric form using given points.

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <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 s ts 1. %3D (y – x) dx…

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Q: To evaluate the integral fx e²dx using integration by parts, the best choices for u and dv are: Oue,…

A: The objective of the question is choose the correct option for integration by parts.

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 along the path C given by x = 2t, y = 4t, where o sts 1. (y – x) dx +…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Evaluate the line integral Lav where C is given by the line y = lnx, 1 ≤ x ≤e. xy ds,

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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 path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [ (v - x) dx +…

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

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Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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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: Verify Green's Theorem by evaluating both integrals y dx + x2 dy = JR dA dy for the given path. C:…

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Q: Use Green's Theorem to compute the line integral | ry? dx – x² dy, -

A: Here we are going to use Greens theorem to find the line integral. Since, to compute the integral…

Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

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Q: What should be i for the path independent of (24) ´ry + A 21y – 1 dy (12) over evaluate the integral…

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Q: Evaluate the given line integral. I (y, –x) · dR, where C consists of 4y = x² from (-2, 1) to %3D C…

A: Line integration of the function

Q: Evaluate the line integral Say dx +z dy, where C is the line segment from (-1, 1, 2) to (2, 3, 1).

A: Evaluate the line integral ydx +zdy where C is the line segment from (-1,1,2) to (2,3,1). Here i…

Q: Show that in the following problems, the line integrals are independent of path of integration and…

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Q: Set up an integral for the length of y = vx + 2, 2 2 <x<7 using ds = 1+ ) dy. A. ds = f, /1+ 4y²dy…

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Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: We have a paraboloid, and each cross section is a circle, parallel to the plane x = 5. We use…

Q: 2. Evaluate the given line integral, (x – y, y) · dR, where C is the line segment from (0, 1) to…

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Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y? + 5z2 and the…

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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 triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

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 = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

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: Evaluate the line integral Scy dx + x dy where C is the parameterized path x = t°, y = t³, 1 < t< 3.…

A: follow next step

Q: Evaluate the line integral cy dx + x dy where C is the parameterized path x = y = t° , 2<t< 6. Scydx…

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Q: The line integral x dy – y dx Jc x2 + y? is independent of path.

A: Given integral is ∫Cxdy-ydxx2+y2.

Q: Use the Fundamental Theorem of Line Integrals to evaluate fo F·dR, where F(x, y) = (x²y² – 3x, r³y)…

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Q: Evaluate the line integral IF.då over the path C to Q (2,4) from P(0,) where F(xy) = 2xy2 + 3y f 131…

A: According to question, Given function, F→x, y = 2xy2 i^ +3y j^,We have to calculate line integral…

Q: Find the line integral along the given path C. Ju- |(x- y)dx, where C: x = t, y = 5t + 6, for 0 sts2…

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Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the…

A: The objective is to evaluate the triple integral ∫∫∫E8xdV, where E is bounded by the paraboloid…

Q: Verify Green's Theorem by evaluating both integrals √( 1² dx + x² dy = √ √ (2x - 3M) JA dA əx ду for…

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Q: Evaluate the triple integral. 5xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A: The point of intersection of the cylinder x=y2 and y=x2 is 0 and 1.

Q: Use Green's theorem to evaluate the closed line integral: . x²y dx +x'y dy along C between -1 < x< 2…

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Q: Use Green's Theorem to evaluate the line integral (у — х) dx + (2х — у) dy for the given path. C:…

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Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

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Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: We have  I=∫(0,0)(3,5) cosh(x23+y25)(10xdx+6ydy)apply Green's…

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the…

A: here, E is bounded by the paraboloid  x=7y2+7z2  and the plane x=7.    so , at    x=7 ,     y2+ z2…

Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and the…

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

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Q: Evaluate the triple integral,   4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and…

A: To calculate the value of the triple integral under the given terms

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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