Use the given transformation to evaluate the integral. (3x + 12y) dA, where R is the parallelogram with vertices (-1, 2), (1, –2), (4, 1), and (2, 5) ; 글(u + v), y= 글(V- 2u) X = 3

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: Convert the integral  0∫2 0∫2z y∫2y dxdydz in the order a) dzdxdy b) dxdzdy

A: Given: ∫02∫02z∫y2ydxdydz

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

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Q: Evaluate on B region using the transformation 11=xy and v = x-y y= 4 ールーアー1 2-7-9 O a -8 Ob. 8 Oc2…

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Q: Use the given transformation to evaluate the integral. | &x +y) d4, where R is the square with R…

A: To find- Use the given transformation to evaluate the integral. ∬Rx + y dA, where R is the square…

Q: (d) Show that the function T: R2 - R? defined by T(Vi, v2) = (vi-v2, vi +2v2) %3D is a linear…

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

A: Given that vertices of parallelogram is −3,9,3,−9,4,−8  and −2,10 And transformation is x=14u+v  and…

Q: Use the given transformation to evaluate the integral.   (15x + 15y) dA   R,  where R is 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: Use the given transformation to evaluate the integral. || 2 Y dA, where R is the parallelogram…

A: Given, ∫∫Rx-4y6x-ydA Where R is the parallelogram enclosed by the lines x-4y=0,x-4y=2 and…

Q: Use the given transformation to evaluate the integral. || (x+y) dA, where R is the square with…

A: Given: vertices of the region square (0, 0), (4, 6), (6, -4), (10, 2) As x=4u+6v      y=6u-4v…

Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

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Q: Use the given transformation to evaluate the integral.   (9x + 12y) dA   R,  where R is the…

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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. Il (ax2 - 9xy + 8y2) da, where R is the…

A: Given integral is, ∫∫R(8x2-9xy+8y2)dA              Given that, x=37u-325vy=37u+325v

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

A: Consider the given integral, ∫∫Rx-3ydA and consider the given transformation, x=8u+vy=u+8v so, the…

Q: Use the given transformation to evaluate the integral. 6x2 dA, where R is the region bounded by the…

A: Evaluation of the double Integrals,

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 given integral, where R is the triangular region with…

A: To find the integral using given transformation .

Q: Use the transformation u = y - x, v = y, to evaluate the integral on the parallelogram R of vertices…

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Q: Use the given transformation to evaluate the integral, where R is the parallelogram bounded by the…

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Q: Use the given transformation to evaluate the integral. 3x dx dy, u = x+ y, v = - 2x+y where R is the…

A: To evaluate the double integral using change of variable follow: Determine the region under a given…

Q: The transformation T : R? → R² defined by T(u, v) = (u – v, 2u – v) carries the rectangle R with…

A: Given The transformation T:R2→R2 defined by Tu,v=u-v,2u-vCarries the rectangle R with vertices 0,0,…

Q: Use the given transformation to evaluate the integral a) SSp(4x +8y)dA where R is the parallelogram…

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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: Use the transformation u = y - x, v = y, to evaluate the integrals on the parallelogram R which has…

A: We need to evaluate the integral: ∬Ry-xdA using the transformations: u=y-x, v=y. Here, R is a…

Q: Show that the transformation 1 W = transforms the upper half-plane into the interior of a square…

A: It is given that w=∫0zdξξ3-ξ12=∫0zdξξξ2-1 Use the substitution ξ=cosecθ,dξ=-cosecθcotθdθ also for…

Q: Find // (3x + 5y)dA where R is the parallelogram with vertices (0,0), (4,2), (-1,5), and (3,7). Use…

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Q: Use the two properties L1 and L2 to show that the following are linear transformations. VI (c) T:R³…

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Q: Use the given transformation to evaluate the integral. + v), y = v - 3u) (16x + 16y) dA, where R is…

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Q: Use the given transformation to evaluate the integral. (x – 6y) dA, where R is the triangular region…

A: Transformations: x=5u+vy=u+5v Vertices are (0,0), (5,1) and (1,5) By these three points we get the…

Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

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Q: Use the given transformation to evaluate the integral. u + v), y = v (16x + 16y) dA, where R is the…

A: Given  ∬R16x+16ydAWhereR is the parallelogram with vertices -3,9, 3,-9, 4,-8, -2,10and x=14u+v ,…

Q: 2) Use the change of variables formula and an appropriate transformation to evaluate ff, xy dA where…

A: Jacobian is for n functions in n variables, the Jacobian is the determinant of the Jacobian matrix.…

Q: Which of the following transformations are linear? А. Т В. Т 8 x + 2 С. Т y, D. T z. 7y Е. Т -4z -9x…

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

A: Let us consider the integration I=∫R∫f(x,y)dxdy Change the variable to x=f(u,v)y=g(u,v) The integral…

Q: Use the given transformation to evaluate the integral.   (15x + 10y) dA    , where R is the…

A: Given integral I=∬15x+10ydxdy R is the parallelogram with vertices -2,8, 2,-8, 3,-7 and -1,9…

Q: Use the given transformation to evaluate the integral f. (4x + 8y) dA where R is the parallelogram…

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Q: 2. Use the transformation u= x – 2y, v = 2x + y to find S x- 2y dA (4) 2.x + y Where R is the…

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Q: Find (3x + 4y)dA where R is the parallelogram with vertices (0,0), (-1,4), (-4,-2), and (-5,2). R…

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Q: Write the expression for a linear transformation T: R2 → R?. whose null space be the straight y=3x

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Q: Use the transformation (change of variables) x = 2u +v and y = u+ 2v to set up the integral / (x –…

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Q: Use the transformation x + y = 2u, x − y = 2v to evaluate the integral 1-[[√²²-²44 √x² - y² dA I = D…

A: We find required value of integral.

Q: Use the given transformation to evaluate the integral. 8x2 dA, where R is the region bounded by the…

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Q: b) Use the transformation u = 2x – y, v = x + 3y to find JfR dA, x+3y where R is the rectangular…

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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 integral. (9x + 9y) dA, where R is the parallelogram…

A: This question is based on the concept of change of variables in double integral whose formula is…

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

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