•π/2 1 [™ ² + xy cos(x²y) dx dy

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

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Q: Use U-Substitution fo evaluate the integral,

A: Given: ∫2x3x2-13dx To find: We have to solve the given integral using u-substitution.  Required…

Q: Using the substitution u = 1+x^2, convert the integral into one involving only the variable u. You…

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Q: 2a 1.² 1.²² 0 2ax-r² dydx

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Q: Find the value of w = 5 bounded by y = 0, y = 2,0 ≤x≤ 2y, and x ≤z≤y + 4.

A: We have to find the value of w=5. It is bounded by:y=0, y=20≤x≤2yx≤z≤y+4

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

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

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Q: = 2* and the chord joining the poin Ans. 5- 3/n Find the area between the curve y (0,1) and (2,4).…

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Q: Use Table shown to rewrite as the difference of two integrals.

A: Given integral, ∫162x3-4xdx          ...(1)

Q: Why does Hm have minus x in front of it. How did they do integral?

A: Both the questions are explained in step 2.

Q: 2a 12²0 So 0 0 2ax-x² dydx

A: Given: I=∫02a∫02ax-x2dydx For evaluating given integral need to use formulas mentioned below…

Q: 21.3 xdx V16 - 9х4 0.

A: We to integrate the given integration.

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: 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: 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: (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…