Question

The area under the curve $y=\sqrt{x}$bounded below by the $x$-axis and on the right by $x=4$is $\frac{16}{3}$square units. Using the ideas presented in this section, what do you think is the area under the curve of $y=\sqrt{-x}$bounded below by the $x$-axis and on the left by $x=-4$ ? Justify your answer.

Short answer

The area is same for both the functions

Step-by-step solution

Given information

Given the equation$$\begin{gathered} y=\sqrt{x}, \\ y=\sqrt{-x} \end{gathered}$$

Checking the areas

The graph is

Checking the area

The graph of $y=\sqrt{-x}$is

The graphs are reflection of each other so the area is same for both the functions