MHB Integral - cylindrical coordinates

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The discussion focuses on finding integration limits in cylindrical coordinates for a volume defined by the cylinder y² + z² = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant. Participants suggest various integration orders and limits, emphasizing the need for the limits to depend on the variables of integration. The correct integration setup is identified as integrating z from 0 to 3, θ from 0 to arctan(3), and r from 0 to √[(3 - z²)/sin²(θ)]. There is also a consensus that inserting z into the integrand is essential for correctly computing the integral. The conversation highlights the complexity of visualizing the 3D region and the challenges of using cylindrical coordinates effectively.
  • #31
I understood, thank you guys =)
 

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