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?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.