Consider the circle defined by

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

Problem

x^{2}+y^{2}=4y

. When computing the area of the portion of this circle that lies to the right of the

y

–axis using horizontal slices, one rewrites the equation in the form

x=f(y)

. Identify which branch of the resulting function

x=f(y)

must be selected and briefly explain why that branch is appropriate for the calculation.