Suppose a curve is described by

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

x = f(y)

, where

f(y) \ge 0

for

a \le y \le b

. Which of the following expressions represents the area of the region bounded by the curve and the

y

-axis? (a)

\displaystyle \int_{a}^{b} f(y)\,dx

(b)

\displaystyle \int_{a}^{b} f(y)\,dy

(c)

\displaystyle \int_{f(a)}^{f(b)} y\,dx

(d)

\displaystyle \tfrac12\int_{a}^{b} f(y)\,dy