SLo(xy) dA where R is bounded by 9x2 + 4y² = 36 %3D Use the transformation: x = 2u and y = 3v

Q: Evaluate the iterated integral. LLL- 2 x³ y2 + z?dxdydz 0.

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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: DGiven SS dy dx. Reverse the order of integra tron and evaluate. Stow THE REGION,

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Q: Evaluate ∭E sqrt(x2+y2) dV where E is the region that lies inside the cylinder x2+y2=4 and between…

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Q: Evaluate the double integral. (2х + у) dA, D = {(x, y) | 1<ys 4, y – 3 <x< 3}

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Q: Evaluate 5² dV where E is the region below zx +2y + 4z = 8 in the first octant. Da B

A: Given problem:- Evaluate  ∫∫∫E  5x2dV where E is the region below x+2y+4z=8 in the first octant.

Q: Evaluate p (x² – 2xy)dx + (x²y +3)dy around the boundary of the region defined by y? = 8x and x = 2…

A: To evaluate : ∮x2-2xy dx+x2y+3 dy around the boundary of the region defined by y2=8x and x=2 (a)…

Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

Q: 2. y(x-y²)dx + x(x++y²)dy = 0

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Q: Calculate (x²+y²) dx dy area when D is the limited to x²-y²=1, x²-y²= 9, xy = 2, xy=4

A: As per the question we are given a double integral over the 2d region D bounded by the following…

Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

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Q: Use symmetry to evaluate the double integral. 4xy 1+ x2 dA, R= {(x, Y) | -4 s x s 4,0 s y s 1}

A: When the upper and lower limits of definite integrals become same, the result is zero irrespective…

Q: Evaluate E=∭D(x2+y2+z2)−3/2dV where D is the region bounded by the surfaces x2+y2+z2=9 and…

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Q: 2. Evaluate fff 12ydV where the limits of integration is the region below 6x + 4y + 3z = 12 in 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: In the following exercises, use the transformation y-x=u, x+y= v to evaluate the integrals on the…

A: Introduction: In mathematics, integration is a technique for combining or adding parts to arrive at…

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: xy2 to compute fpxy2 dA, where R is the region bounded by ry 2, xy = 7, xy2 = 2, xy2 =7 Use the…

A: Given,

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. | 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: ·볼+1 2x - y dx dy, Use the transformation to evaluate 2x-y where u = v = % and integrating over an…

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Q: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

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: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

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: Let T be the triangular region bounded by the lines y = x,0 <x <1. By using the transformation x = u…

A: Let T be the triangular region bounded by the lines y=x, 0≤x≤1. Given transformation x=u+v and y=u-v…

Q: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: Find the Jacobian of the transformation. x=u/v, y=v/w, z=w/w, and evaluate the double integral of…

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Q: 15. Use the transformation x = u/v, y = uv to evaluate the integral sum ~4 r4/y (x² + y²) dx dy +…

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Q: Use the transformation u = y – r and v = y to evaluate the integral // 2 + s°) dz dy where R is…

A: Solve it.

Q: Evaluate the triple integral 3 4 (y/2)+1 SS S (+) dr dy dz 00 y/2 in ryz-space by using the…

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Q: Q2/(a): Evaluate the double integral , 3xy dA over the rectangle dA = dydx} R {(x, y): -3 x< 2,…

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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 transformation x = u + (1/2)v, y = v to evaluate the iterated integral ry=2 x=(y+4)/2 y³(2x…

A: Let us consider the function x=g(u,v) and y=h(u,v) The Jacobina is obtained as J=∂(x,y)∂(u,v)

Q: - Zvw (sin ( 8. Use the transformations v = x + y and w = x – y to set up the transformed integral…

A: For the solution follow the next steps.

Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: Evaluate 7x dV where E is the region that lies inside the cylinder x2 + y² = 8 E and between the…

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Q: Evaluate fff 12y - 8x dV wherein the limits of integration are the region behind y = 10-2z and in…

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Q: Evaluate the line integral. L(4x – 8y) ds C:x + y = 100 (4x - 8y) ds = i |

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

A: According to the given information, It is required to calculate the given integral using the given…

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: O R is the region bounded by y = 2 – x² and y = x² – 6. - %3D

A: 5.)  y=2-x2  and  y=x2-6 red line y=2-x2 blue line y=x2-6

Q: Consider the integral x³+1 x³(x²+1) -dx What is the correct partial fractio OA Bx + C

A: We have to choose the correct option from the given options according to the given information

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: Find the double integral ff (x² + y² do, over R={(x, y):-1≤ x ≤ 1,0 ≤ y ≤ 2}. 1.

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

Q: Q1 Verify that [(v ²– 2x )dx +(2xy +x³\dy = | dA where C is the boundary of a region %3D дх ду R…

A: By  apply green theorem

Q: Evaluate III Vx2 + y² dV E where E is the region that lies inside the cylinder x2 + y2 = 4 and…

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