Compute the integral of f(x, y) = 4xy over the region D = {(x, y) | 1 < x² + y² < 4, y > 0, y 2 x} Select one: O a. 3 8 O b. 7 - 4 9 С. 8. O d. 11 2 15 е. 4

Q: integrais AN ам Lyox+x2ay-L IN-am) ад y2 dx + x2 dy dA ?х ду r the given path. R C: square with…

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Q: VIII. Let f(x,y,z) = xe" +z? and F(x,y,z) = (xy, x²yz, yz). Compute 1. Div(grad(f)) 2. Div(curl(f))…

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Q: 6- Evaluate the line integral fe F dr, where F = [ry, yz, r2] and C is the boundary of the…

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Q: Calculate the line integral of F(x, y, z) = (e², e, e) over the path from P = (0,0,0) to Q = (-6, 6,…

A: We have to calculate the line integral of F(x, y, z) = (ez , ex-y , ey) over the path from P =…

Q: () 4 dædydz; V: {r+y+ z = 3; x 20; y 20; :> 0} O A. pi В. 3 С. б D. 9

A: The given integral is ∫∫∫V43-xdxdydz and region is x+y+z=3; x≥0 ,y≥0, z≥0

Q: z dV, B (x – 1)2 onde B := {(r, y, x): (y – 1)² + 22 < 2z 4

A: Here is the solution of the given problem. Volume integral:

Q: Q4A) Find area bounded by y = 0.y = √2x-x² using double integration.

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: Q6) valuate the integral as f(x, y, z) = (1+ rks) = cos(2t) i+ sin(2t)j+ tik ;0sts 2n.

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Q: Find the Cauchy principal value Lant dx (x+1)(x²+2) -R of the following integral R

A: We have to find the Cauchy principal value of given integral.

Q: Evaluate the integral F· dr. F(x, y) = (7x2 + y) i + (8x – cos y) j where Cis the boundary of the…

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Q: What should be A for the path independent of (2,4) 2Ay – x dy. y? XY + A (1,2) over evaluate the…

A: Consider the provide integral,

Q: (2) Find the integral (0,2,0) and (0,0,1). where D is the tetrahedron with vertices (0,0,0),…

A: Given : ∬∫x+2y+z dV             where D is  tetrahedron with vertices 0 ,0 ,0  , 1 , 0 , 0  , 0, 2 ,…

Q: Evaluate the integral (xy + xy²) dx + (2x² + x²y) dy over the curve C, defined by going in a…

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Q: 22. Compute the contour integral (Баллов: 2) Sof (2) dz, z E C, if f (z) = and path is semicircle z…

A: Topic:- application of integration

Q: YA (1,0) C is the path from (1, v2) to (1,0) along line segments as shown in the figure above. Then…

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Q: – 4V5 )ds]

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Q: If the change of variable |ə (x, y) d(u, v) | v v³ (²) = (²+²) u at the point where (x, y) = (2, 3)?…

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Q: 1. Evaluate the integral If. (430 R (4x + 16y)dA, where R is the parallelogram bounded by the lines…

A: To find the given integral , we can change the given integral in  terms of 'u' and 'v' .

Q: noose an appropriate change of variables to c al over a rectangle in the uv-plane.

A: Introduction:   The definite integral can be applied to multiple-variable functions. Consider the…

Q: Let A₁ be the set {(x, y): x² + y² ≤ 1} and let A₂ be the set in R2 bounded by the lines y - 2x = 1,…

A: Evaluation of the double integral using convestion of polar coordinates and conversion of Jacobin…