Let F = yi + xj + x³y³ z³k, C the curve x2 + y² + 6x – 2y + 9 = 0, z = 2 (with counterclockwise orientation looking from the direction of the positive z-axis). Calculate the line integral - F· dR. C

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A: To find the line integral, obtain dS as follows.

Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z over the curve c(t) = (e',…

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Q: Evaluate the line integral F(x, y) = xyi – y²j where the curve C is repre sented by R(t) =t²i+t³j…

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A: We will find out the required solution.

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A: Consider the given:…

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A: Given line integral is,

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Q: Let f= ed -xy, F=Vf and C a Curve Parâmetrized by r(t) = 4?;- tj, 14t<2 Compute the Zuie %3D %3D…

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Q: Compute the line integral of the scalar function f(x,y,z)=2x2 +8z over the curve…

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A: Introduction: Green's theorem is one of calculus' four fundamental theorems, all of which are…

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Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z ver the curve c(t) = (et, t2…

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Q: Evaluate the unoriented line integral +y² + z²) ds along the parametric curve a : [0, 1] → R³ with…

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Q: Compute the line integral of the scalar function ƒ(x, y, z) = 2x² + 8z over the curve c(t) = (e¹,…

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Q: Evaluate the line integral ſp(xi + Vyi) · dr where D is the oriented curve shown below. (1,1) y = x2…

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A: According to the given information, it is required to evaluate the line integral.

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Q: Compute the line integral (yze"y= + y² + z – 2x) dx + (xze"v² + 2xy) dy + (xye"y= +x+ 3z²) dz C…

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Q: Evaluate the line integral F dr, where C is given by r(t) = (t², t, vT), 0<ts2 and (x, y, z) = (z,…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

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Q: A) if F=2yi-zj+xk evaluate line integral Fxdr along the curve x=cost,y=sint,z=2cost from t=0 to…

A: Given x = costy = sintz = 2cost As F = 2yi-zj+xk Then F(x,y,z) = 2y , -z , x Thus F(x(t) , y(t) ,…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

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Q: Compute the line integral [(yze²v² + y² + 2 − 2x) dx + (xze²v² + 2xy) dy + (xye²³² +x+32²) dz, where…

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Q: Let F = ( ) and y = {x² + (y – 2)²) = 1 with anti-clockwise orientation. Find line integral , F. ds.…

A: Put x = cost  dx = -sint dt y=sint+2   dy = cost dt int(f.ds)  = int (  y/(x^2 +y^2) dx -…