Without drawing a graph

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Without drawing a graph, consider the region enclosed by

y=x^{2}+1

y=4

, and the lines

x=0

and

x=1

. When this region is revolved about the

x

-axis, are the resulting cross-sections filled circles, hollow rings, or a combination that changes along

0\le x\le1

? Explain your answer in one or two sentences.