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Q: Let F(x, y, z) = y° z°i+ 2xyz³j+ 3xy° z²k. (a) Find the domain of F, and show that F is…

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Q: Evaluate the following triple integral over half unit ball below y-plane(B), //| Væ² + y? + 2² dV. B

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Q: xyzdV where E is the solid: 0 < z < 8 ,0< y< z ,0<x < y.

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Q: (y dx – x dy) (x³ + 2xy² + x?y + y°) = 0, y(1) = 1

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Q: 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the…

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Q: 2x2 dv, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0,…

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Q: SSS (x+ yz?) dx dy dz v. 06x< !, 0£ys2

A: Given that ∫∫v∫x+yz2dxdydz, where v:0≤x≤1, 0≤y≤2, -1≤z≤3 Here, we will evaluate the given integral

Q: 8. (x – y) dV, where E is enclosed by the surfaces z = x² – 1, z = 1 – x² , y = 0, and y = 2 E

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Q: sin z dz, C (z+1)7 tan (z/2) ii) J. dz C Z-T/2

A: To Solve the above integral we use Cauchy Integral Formula.Given in Second Step.

Q: Find integral fraction (numerator) y dy / (denominator) square root of (y+2) using the substitution…

A: Let's find given integration by using given substitution.

Q: Find the volume of the region = {(x, y, 2) : æ² + y² – 3 < z< V9 – a² – y²} E - -

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Q: /6х — 22

A: We will evaluate the given integral as shown below by using trigonometric substitution

Q: ) (2xy+y2) dx - 2x2 dy = o 2) xy dx-(x + zy)? dy = o メ+ 2y)? dy

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Q: 6x? + Sx t 16 dx +2x +6 x + 3? a.Sinlat3l+; 4 Cが)返が)+c er none

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Q: 2y*+1 dy 3

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Q: Integrate: - da 9x2+16 O In (3x + v9x2 +16) + C O In (3x + V9x2 +16) +C ㅇ tan ' (뚜) + C 0 tan1 (부) +…

A: Given ∫dx9x2+16

Q: Evaluate / (x* – 2y) dA where D = {(x, y) E R²| – 1 < x < 2 and – x² < y < x²}. -

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Q: find area, y=2x , y=3-x2  (0,1)

A: Area is a 2-dimensional quantity which is the measure of amount of space covered by any shape in a…

Q: Differentiate, hcx) = In (x-Vr

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Q: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: dx (16+x?,2

A: To find:

Q: Use integration by parts to evaluate |6xe* dx. (7x+1)(6e*) +C A) бе 49 B) -7x e +C 7 | C) (6e"*) -7x…

A: givenI=∫6xe-7xdxif u=x and v=e-7xthen we use integration by parts Formula∫uvdx=u∫vdx-∫[ddxu∫vdx]dx+c

Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

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Q: Evaluate the integral cot5 x csc3x dx O Lesc" x - ese" x + cse" x - c 2 csc' x + 5 글csc3 x + C 1 X +…

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Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: udx + (1 - 3u)x du = 3u du.

A: I have stated the used formulas in the solution

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…