We know that Sclf(x,y)dx +g(x, y)dy] = Sf(x, y)dx + S, g(x,y)dy. Use Sef(x,y)dx + S g(x, y)dy. Use %3D this knowledge to evaluate . (y dx + x dy) where C is the line segment from (1,-1) to (4,3).

Q: Evaluate (2x - y) dx + (x + 9y) dy. C: x-axis from (0, 0) to (0, -9) and (0, -9) to (4, -9)

A: Solution :-

Q: xydy – (y² – 3x²) dæ = 0

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Q: If C is the line segment connecting the point (a1, b1) to the point (a2, b2), show that 3r dy – 3y…

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Q: √ ² S ² (2y² + x² + 3) dy dx 0

A: Given integral, ∫02∫012y2+x2+3dydx The objective is to evaluate the integral.

Q: Evaluate 112x ·x) dx = (2x - y) dx + (x + 5y) dy. C: x-axis from x = 0 to x = 6

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Q: Find Vƒ(P) and D7f(P). (a) f(r, y, 2) = yf + z² – 4xz; Ū = } i – $ j+ k; P(-2,1,3)

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Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) 21

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Q: Evaluate Jo (2x - y) dx + (x + 5y) dy. C: x-axis from x = 0 to x = 6

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Q: x y ● = Find the dot product of 1 18 0 — -2 and y = 1 2 4 ●

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Q: 20. Find all the intercepts of y = 4x (1 - x²) A) (- 1, 1) B) (±1,0) and (0, 0) C) (0,0) D) (0,0 )…

A: We can determine all the intercepts as below

Q: Evaluate -42 (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) X

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Q: Find an equation for the contour of f(x, y) = 2a²y + 6x + 15 that goes through the point (4, 1).…

A: A contour line of the quadric surface is the curve of intersection of the quadric surface with the…

Q: -5/2 y?-2y 4. -/2 - 2y 1/2

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Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 323 2

A: Here to find the value of line integral we consider two path c1 :from the point (0, 0) to (0, -7)…

Q: Find point P(x,y) if it is equidistant between points A(2,9) and B(-3,6)

A: Given:-  Px,y is equidistant  from the points  A2,9  and  B -3,6 i.e,  AP=BP and  we know  that…

Q: shows the image of (D2 • Ry-axis)(4, -3)?

A: D2∘Ry-axis4,-3 this means 4,-3will be reflected over the y-axis. And then it will be dilated by 2.…

Q: dy 3(x+y+1)2-(x +y- 1)² dx

A: Given :

Q: Evaluate (2x - y) dx + (x + 3y) dy. JC C: x-axis from (0, 0) to (0, -3) and (0, -3) to (9, -3)

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

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Q: dy : Find if dx 3.x 2) x - y 4+ y x +y 4) xy² x - y

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Q: ScF· dĩ, where F(x,y) = (6x - 2y)7+x²7, and C is the line segment Evaluate from (6, -3) to (0, 0).

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Q: If 2x = xy + y2, then A. C. -2 + y x + 2y (2-y) x + 2y dx 11 B. D. -(2 + y) x + 2y -(-2+ y) x + 2xy

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