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?
by
Chan Lye Lee