Consider a planar region that is subdivided by the vertical line into two…
MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider a planar region that is subdivided by the vertical line x=1 into two non-overlapping subregions, R1 on 0≤x≤1 and R2 on 1≤x≤3. The combined region is revolved about the x-axis to form a solid S. In one or two sentences, explain why the volume of S equals the sum of the volumes generated separately by R1 and by R2.