# Area under the curves, can you make a right choice?

Calculus Level 2

Take a point $$A$$ on the graph of $$y=f(x),$$ and let $$B$$ be a point on the graph of $$y=\sqrt{x}$$ such that $$AB$$ is parallel to the $$y$$-axis. Call the area bounded by these two curves and the segment $$AB$$ as $$R.$$

Now, let $$C$$ be a point on the $$y$$-axis such that $$AC$$ is parallel to the $$x$$-axis. Call the area bounded by the curve $$y=f(x),$$ the $$y$$-axis, and the segment $$AC$$ as $$S.$$

Given that the function $$f$$ is continuous and the areas $$R$$ and $$S$$ are equal, which of the following statements is true?

×