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How Solve a Triple Integration

Problem:

Solve the following integration.


 
where V is limited by the surface x2 + y2 = 2z

The integration region is restricted within the paraboloid by the plane z = 2.


As the projection of the region on the z = 0 the plane is the circle C: x^2 + y^2 ≤ 4, the triple integral can be decomposed so as:



Writing the integral in cylindrical coordinates, we obtain:



This is the process to solve a triple integration using the cylindrical coordinates.

I hope it has been helpful.

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