We know that S(x,y)dx + g(x,y)dy] = Se f(x,y)dx +Seg(x,y)dy. Use this knowledge to evaluate S.y dx+x dy) where c is the line segment from %3D (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: IX. Į F dF where F = (x,y) and C is the straight line from (2,3) to (4,0)

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Q: Find fa, fy, fyx and fy if f(x, y) = x + y + xy ух

A: This is second partial derivative so do the derivative like normal considering all other variable…

Q: y? + 2xy + x³ = 3y.

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Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: y = x + C,e* + C,e-2*

A: y=x+C1ex+C2e-2x

Q: XI. 6 F dF where F = (x³ – y, x + e') and C is triangle with vertices (0,0), (3,0), (4,2).

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Q: . Evaluate JVy³ + 1 dydx

A: Given,          ∫01∫x1y3+1dydx

Q: Let X: EXP(0). suppose Y= 2x , the Y is i = 1 Select one: a. Gamma (n,-) b. Camma(n. 4) С.…

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Q: Identify the prey and predatory from the following Equations a) dx/dt=-0.06X+0.0002xy…

A: Given two differential equations We have to find out prey and predatory from the following…

Q: CHON With c 1 = 0.0001. 3. Consider the function (x-1)^2 + (y-1)^4, which obviously has a minimum at…

A: As per the question, we consider the optimization of a multivariate polynomial function :f(x,y) = (x…

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: 2 2dx 9+4x? 2

A: Here we have to find the value of the given integration.

Q: Find the values of w, x, y, z and Dx x + y + z + w = 13 2x + 3y - w = -1 -3x + 4y + z + 2w = 10…

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Q: If fxy (x, y) = , ,0 2) =

A: Given,fXY(x,y)=x+y27 ; 0<x<2 , 3<y<5

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: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

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Q: 2 The Range (Ry) of y = v9 – x² -

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Q: Find f, (8,2) if f(x.y) = e* - 5y.

A: We can find the answer as below

Q: Evaluate [1+(x- 1)2 +4y²]dydx

A: Given: The given integral is ∫03∫021+x-12+4y2dydx. Integrate the integral with respect to y.…

Q: dw Find ду dw at the point (w, x, y, z) = (3, - 1, - 1, - 1) if w = x3y? + yz-z° and x2 + y? +z? =…

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Q: 1 √x y³+1 2 Sőt. S²/E 0 dydx

A: We are given an integral. Our aim is to evaluate the integral ∫04∫x21y3+1dydx.

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: 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

A: