Use the given transformation to evaluate the integral, where R is the parallelogram bounded by the lines y = -x+1, y = -x+4, y= 2x+ 2, and y = 2x+ 5. (-3x + 5y) dx dy; u=x+y, v= - 2x+y R 71 O A. 91 O B. 91 OC. 4 71 O D. 4

Q: Consider the function f: R2 -R, find the integral of f (x, y) = x + y along the path x (t) = (2cost,…

A: We have to find the integral of f (x, y) = x + y along the path x (t) = (2cost, 2sint) with tÎ [0, π…

Q: By making an appropriate change of variables, evaluate the double integral I - [[ (7 + v)e=" »° dzdy…

A: By making an appropriate change of variables, evaluate the double integralI=∬R(x+y)ex2−y2dxdywhere R…

Q: Use the transformation u = 3x + 4y, v=x+4y to evaluate the given integral for the region R bounded…

A: Formula Used: ∫∫Rf(x, y) dxdy=∬f(u, v) J du dv

Q: Use the given transformation to evaluate the integral. 7x2 dA, where R is the region bounded by the…

A: x=5u, y=6vThen 36x2+25y2=900 becomes36(54)2+25(6v)2=90090042+900v2=900⇒…

Q: Evaluate the integral f. x'y°dy – x³y?dx, where C is the square determined by the 0, y = 0, x =…

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Q: Evaluate the line integral 2 Cx2y)dx- 2xdy along each of the following closed paths, taken…

A: Given that the integral,

Q: Use the given transformation to evaluate the integral, 3x2 dA,  where R is the region bounded by the…

A: The given region R is an ellipse, transform the same using x and y as follows.

Q: Which of the following integral will we obtain when we rewrite the integra 4 1 [F cos y dx dy by…

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Q: Use the given transformation to evaluate the integral. 8y2 dA, where R is the region bounded by the…

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Q: Evaluate the line integral xyz ds where C is the line segment joining the points (1, – 1, 1) to (1,…

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Q: Find the line integral of F = (6x - 3x) i+3z j+k from (0,0,0) to (1,1,1) over each of the following…

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Q: Use the given transformation to evaluate the integral. || 5x? dA, where R is the region bounded by…

A: Solve the double integral bounded by ellipse,using Jacobin transformations

Q: Use the given transformation to evaluate the integral. Zv2 dA, where R is the region bounded by the…

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Q: Use the given transformation to evaluate the integral. 7x2 dA, where R is the region bounded by the…

A: Given : R is the region bounded by the ellipse 9x2+25y2=225 given transformation x=5u,y=3v We want…

Q: Evaluate the given integral by making an appropriate change of variables. JJ₂ ³ 3 x - 8y dA, where R…

A: To Evaluate: The given integral by making an appropriate change of variables ∬R3x-8y3x-ydA, where R…

Q: Use the given transformation to evaluate the integral. || 2y dx dy, u=X+ y, V = - 2x+ y R where R is…

A: short summary:  Firstly we can draw a parallelogram bounded by the given lines and find intersection…

Q: se the given transformation to evaluate the integral. J 6z + 3ydA, where Ris the parallelogram with…

A: we have given: x=13u+v and y=132u-v  u=x+y, v=2x-y Now, Consider the integrals, ∬R6x+3ydA where, R…

Q: Use the given transformation to evaluate the integral. u = -2x + y, v= 5x + y; SS (5x + y) dx dy,…

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Q: Evaluate the integral / (x + y)e*²-y° dA by making an appropriate change of R variables where R is…

A: …

Q: Use the given transformation to evaluate the integral. I| 7(x + y) er - y² da, where R is the…

A: Given that, the rectangle is enclosed by the lines x-y=0,x-y=5,x+y=0 and x+y=10. And also given…

Q: Use the given transformation to evaluate the integral. JJy d4, where R is the region bounded by the…

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Q: Use the given transformation to evaluate the integral. | 5x2 dA, where R is the region bounded by…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the transformation u = 3x + y, v=x+3y to evaluate the given integral for the region R bounded by…

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Q: Use the given transformation to evaluate the integral. 11² 9x² da, where R is the region bounded by…

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Q: Use the transformation u = 2x + y, v = x + 4y to evaluate the given integral for the region R…

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Q: Use the given transformation to evaluate the given integral, where R is the triangular region with…

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Q: se the given transformation to evaluate the integral. 3xy dA, where R is the region in the first…

A: We have to evaluate the integral bounded by given lines and hyperbola curves.

Q: Evaluate the triple integral -6 (x – 3)³ (y + 13)² (z – 2)4 - dz dy dx 8 49 625 3 by using the…

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Q: Use the given transformation to evaluate the integral. 8xy dA, where R is the region in the first…

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Q: Use the given transformation to evaluate the integral. where R is the rectangle enclosed by the…

A: First consider the transformation that is to be used and find x and y in terms of u and v:

Q: Find the line integral of f(x,y,z) = x+ y+z over the straight-line segment from (2,1,3) to (1, –…

A: Solution: f(x,y,z)=x+y+z

Q: Calculate the integral / F. dr where F(x, y) = (xy? + 3x2y) i+ (x + y)x²j is conservative, and C is…

A: Answer

Q: Use the given transformation to evaluate the integral. 8xy dA, where R is the region in the first…

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Q: Væ – 2 -dx z +1 u = Va – 2

A: We have to evaluate the integral ∫x-2x+1dx by using the substitution u=x-2.

Q: Evaluate the integral using the given substitution. (6(y6 + 2y3 + 1)° 2y5, 2y2) dy,u= y6 + 2y3 + 1 O…

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Q: Calculate the integral of f(x, y) = e*-2y over the parallelogram in Figure 7. y (6, 4) (1, 3) D (5,…

A: Let the given integral, f(x,y)=e3x−2y Now, from the figure of the parallelogram, let O(0,0), A(5,1),…

Q: Evaluate the line integral ScF- dr where F(x, y) = (5x + 4y)i + 3xyj and C: r(t) = 3ri + rj, 0sts1 O…

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Q: Use the transformation T : (u, v) → (x, y) with 1 1 3(u + v), y = 3(v – 2u), to evaluate the…

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Q: Use the given transformation to evaluate the integral. || 10y2 dA, where R is the region bounded by…

A: Given the given integral is ∫∫R10y2dA, Where R is the bounded by the curve xy=2, xy=7, xy2=2 and…

Q: Evaluate the given integral by making an appropriate change of variables. X – 7y dA, where R is the…

A: given Integral∬R3x-7y5x-ydA enclosed by lines  x-7y=0,   x-7y=9, 5x-y=2,   5x-y=7 Let x-7y=u and…

Q: Evaluate the given integral by making an appropriate change of variables. 2 = BY dA, where R is the…

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Q: Evaluate the given integral by making an appropriate change of variables. Y da, where R is the…

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Q: Use the given transformation to evaluate the integral ∬R 6x^2 dA where R is the region bounded by…

A: The given region R is an ellipse, transform the same using x and y as follows

Q: Evaluate the given integral by making an appropriate change of variables.   where R is the…

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Q: Use the given transformation to evaluate the integral. Sh 7y2 dA, where R is the region bounded by…

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

Q: Verify Green's Theorem by evaluating both integrals aM | y? dx + x² dy = dA ax for the given path.…

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Q: Use the given transformation to evaluate the integral. IL 3(x + y) e- da, where R is the rectangie…

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Q: Use the given transformation to evaluate the double integral, 7((x-4y)/(7x-y)) dA  where R is the…

A: Obtain x and y in terms of u and v as follows.

Q: Use the given transformation to evaluate the integral, 10 sin(81x2 + 49y2) dA,    where R is the…

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Q: Use the given transformation to evaluate the integral. J (8x + 8y) dA, where R is the parallelogram…

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