Use cylindrical coordinates. Evaluate x2 + y2 dV, where E is the region that lies inside the cylinder x2 + y2 = 1 and between the planes z =-4 and z =-1.

The distance from a chosen reference axis (axis L in the illustration opposite), the angle from the axis to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis are the three dimensions of a cylindrical coordinate system (plane containing the purple section). Whichever side of the reference plane faces the point determines whether the latter distance is expressed as a positive or negative value. The location where all three coordinates may be specified as zero is the origin of the system. The reference plane and axis come together at this point. To distinguish it from the polar axis, the axis is often referred to as cylindrical or longitudinal axis.

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