Q1//A:- +ydA where Ris the trapezoidal region with vertices given by Evaluate 5 5 2 2 2u + 3v and (0,0). (5,0). using the transformation r = and y = 2u-3v. %3D

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

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Q: 4. Calculate the integral (x – 3y) dA where R is the triangular region with vertices (0,0), (2, 1)…

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Q: Q3: Find the centroid of the next shaded area. 4m

A: Solution :-

Q: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

Q: Sketch the region onto which the sector r< 2, t/4<0Sa/2 is mapped by the transformation w= = iz?.

A: 5) In this question, we have sketch the region in the w-plane by using the region in the z-plane.

Q: 1. Use the transformation u = %, v = xy to find || x y³ dA over the region R in the first quadrant…

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Q: a¹y¹2'dadydz, where V is the (6) Using suitable transformations, evaluate closed region in the first…

A: Given the integral  ∫∫∫Vx4y4z4dxdydz Where V is the closed region in the first octant bounded by the…

Q: Rotate the region bounded by y = 6e 2" and y = 6+ 4x - 2x between a = 0 and a = 1 about the line y =…

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Q: Find the Jacobian for the transformation x = 3u + v and y = u+ 3v. NEXT, use this transformation to…

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Q: and y = 2u, evaluate the integral xy³dA where c) Using the transformation x =-; 6u region R is…

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Q: Find the highest and lowest point (x, y, z) along the surface 8x +10y+ 4xy – x² – 2yʻ within the…

A: Given query is to find the highest and lowest point on the curve for the given region.

Q: I need help finding the absolute maximum and minimum values of f on the set D.

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Q: 1. Use an appropriate transformation of coordinates to evaluate xy dA where the region D is enclosed…

A: Special transformation is used to calculate double integral. Given integral is enclosed with the…

Q: Sketch the image S in the uv-plane of the region R in the xy-plane using the given transformation. x…

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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: 2. Let f: R? → R be the function which satisfies for all (x, y) € R² that f (x, y) = xy. Use the…

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Q: Q3// 1. Sketch the region D and Evaluate: [ f(x+y) dA Where D, is the triangle region region in the…

A: Let's solve given double integration.

Q: Find of and Duf to :- f cas,z) = In (x²+zy?+32) atp(-v34) in the direction of ã=-3i-4j-12K. -314…

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Q: Evaluate (y + Vx) dA, where R is the triangular region with vertices (0, 0), (1,0), and (0, 1). R

A: The solution starts from step 2. The information presented below will be helpful to understand the…

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

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Q: Q4 Calculate the integral Se²y-2x (y + 2x)³ da Where R is the region formed by joining the vertices…

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Q: Integrate Xy ed २ over the triangular region with vertices: (0,0), ), (0,8) (0,16)

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Q: 3. Use the transformation u = 4, v = xy to find || ry³ dA over the region R R in the first quadrant…

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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: Find the Jacobian for the transformation x 3u cos v and y = 4u sin v. %3D NEXT, use this…

A: Given, x=3u cosvy=4u sinv

Q: Use the transformation x= v/u, y = uv to find ſf, xy³ dA over the region R in the first quadrant…

A: To find the solution

Q: Use the given transformation to evaluate the integral. (3x2 - 3xy + 3y2) dA, where R is the region…

A: Here by using the given transformation we have to evaluate the integral.   ∫∫R(3x2-3xy+3y2) dA,…

Q: Eraluate: 1. JJR e-(n^²+yv) the eincles of padii 1& 2 dady, R is the region of between.

A: As per the our guideline, we are supposed to solve only first question. Kindly repost other question…

Q: Evaluate fff dv dV where E is the solid enclosed by the ellipsoid E 3 + 8 + 8 = ¹ 62 using the…

A: We will change the equation using given transformation and then find corresponding limits for…

Q: to find the use lagrange Multiplier Point p (x1s,Z) Closest to the origion on the Plane 2x +y - 2=5…

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Q: First question: find using the transformation v = 3x = y,u= 4x+3y, the product of the integral J…

A: Suppose a two variable function f(x, y)  over the region R then under the transformation x=g(u,v)…

Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

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Q: Evaluate (x" +y)dxay on B region using the transformation U= xy and v = x-y y= 2 -7-1 7-7-9 O a. -8…

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Q: Evaluate ff, y? dA, where R is the region bounded by the ellipse 4x +9y = 36. Hint: Consider the…

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Q: Use the given transformation to evaluate the integral. (3x2 - 3xy + 3y2) da, where Ris the region…

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Q: Q4: Find the centroid of the next shaded area. 1m Im 1 Y 1.5m 1m re1

A: Please refer the attached image for complete solution.

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: 5xyz dv, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), and (1, 0,…

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Q: By using an appropriate transformation, evaluate the integral y2\ 1/2 dædy .2 I R. 36 4 when R is…

A: We have to evaluate the given integral.

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: Find the Jacobian for the transformation x = 3u + v and yY= u+3v. NEXT, use this transformation to…

A: We have given transformation x=3u+v and y=u+3v Jacobian J=dxdudxdvdydudydv

Q: What is the Jacobian of the transformation T that arises from an appropriate change of variables to…

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Q: Use the transformation r = 7u + v, y = u + 7v to rewrite | (x – y)dA, where Ris the R triangular…

A: Let's find.

Q: Evaluate JI (x* +y)dxcdy on B region using the transformation 1= xy and v= x²- y xy= 2 = شر هړ. B و…

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Q: Use the transformation x = 4u and y = 2v to evaluate the integral ∯R y^2 dA where R is the region…

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Q: Find the value of a if the centroid of the region bounded by the parabola y² = 4px and the line = a…

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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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