Discussion
Match the region with the natural coordinate system for integrating over it. 1. A rectangle 2. A disc 3. A ball P. Plane polar Q. Cartesian R. Spherical
Answer: D
The boundary of the region should become a coordinate held constant. A rectangle has sides of constant \( x \) or \( y \); a disc has a boundary of constant \( r \) in the plane; a ball has a boundary of constant \( r \) in space, which is the spherical radius. Matching the coordinates to the boundary is what turns variable limits into constant ones
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