Mathematics

Problem

The region is bounded by the parabola

x=y^{2}

, the vertical line

x=9

, and the

x

-axis. Which one of the following single integrals correctly represents its area without the need to split the interval? a)

\displaystyle \int_{0}^{9} \sqrt{x}\,dx

\displaystyle \int_{0}^{3} y^{2}\,dy

\displaystyle \int_{0}^{3}[9-y^{2}]\,dy

\displaystyle \int_{0}^{3}(y^{2}-9)\,dy