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- 1) Evaluate the line integral ∫_c (2x − y) dx − (x+ 3y) dy , where C is a straight line from (1,1) to (3,5), followed by a horizontal line from (3,5) to (5,5).Compute the line integral∫C [2x3y2 dx + x4y dy]where C is the path that travels first from (1, 0) to (0, 1) along the partof the circle x2 + y2 = 1 that lies in the first quadrant and then from(0, 1) to (−1, 0) along the line segment that connects the two points.Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)
- Evaluate the line integral f(x2+2y2)ds for C: the line segment from (1,2) to (4,6)What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the path from A(0,2) to B(4,6)?Let C be the curve which is the union of two line segments, the first going from (0, 0) to (3, 2) and the second going from (3, 2) to (6, 0).Compute the line integral ∫C3dy−2dx.
- Evaluate the line integral ∫Cydx+xdy along the curve y=x2 from the point O(0,0) to the point A(1,1) (Figure 3 above).Evaluate the line integral ∫Cydx+xdy where CC is the parameterized path x=t^2, y=t^3, 2≤t≤4.Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at ( 1 , 0 ) and ending at (3,1).