Let C be the boundary of the region x? + y° < 1 and (x + y)² <1 which is priented counter-clockwise direction. Evaluate the line integral | (y cos(x) – e* – y) dx + (sin(x) +x +e®) dy.

Q: Evaluate the integral (2x+3y) dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A: To Evaluate: I=∫C(2x+3y)dx+(6x-y)dy along the parabolic arc y=x2 from (0,0) to (1,1).

Q: te the line integral c 3 == 1 from A=(2, 0) to (0, -1) Jax + 2xyay where is the arc on the ellipse

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Q: Evaluate the line integral f, F . dr, where C is the curve given by F(t) = 3 cos ti+ 3 sin t j, 0<t<…

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Q: Sc F. dr where F(x.y) = (3x² – 4v)i + (27 + cos(,³))j

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Q: p(x,y,z)=xz²+sin(y) ex e*

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Q: The line integral 2xe" dæ + a²e" dy + (1 – 2²)e¬²² dz is not independent of path.

A: The line integral ∫CF·dr is independent of path if the curl of F is zero, that is, ∇×F=0. Here, The…

Q: Evaluate the line integral (2x + 6)dx + (5y+ x)dy along the curve C: C F(t) = tỉ + 2tj, 0<t<1.

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Q: Find the line integral of F =9xy*ï +(x² + 3),yj over the path L.

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Q: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A: Line integral will be path independent if vector field whose integral we need  is conservative…

Q: Let G(x. y)=x*yi+(y+xy*)j. Evaluate the line integral [G-dr, where Cis the curve x= ť and y=t* for…

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Q: d 1 (arccosh x) dx %3D Vx2 – 1 -

A: Consider the following equation: y=arccoshx x=coshy=ey+e-y2=ey+e-y2×eyey=e2y+12ey…

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

A: Given integral is ∫Cxdy-ydxx2+y2.

Q: 2 + v - , 2+z+ 11. 0. di

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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…