For the circle defined by

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

Problem

x^{2}+y^{2}=16

, a horizontal slice at a fixed value of

y

intersects the curve at two distinct

x

-coordinates. In one concise sentence, explain why an integral set up with respect to

y

must account for two separate expressions for

x

when determining the area of a region bounded by this circle.