Answer
$\dfrac{256}{3}$
Work Step by Step
We are given that $y= 2 \sqrt x$
Here, the area $(A)$ can be expressed as: $A=2 \int_0^{16} \sqrt x \ dx$
In order to solve the above integral, we will use the following formula such as:
$\int x^n \ dx=\dfrac{x^{n+1}}{n+1}+C$
Now, we have $A=2 \int_0^{16} x^{1/2} \ dx \\=[\dfrac{2x^{3/2}}{3/2}]_0^{16}\\=[\dfrac{4x^{3/2}}{3}]_0^{16} \\=[\dfrac{4(16)^{3/2}}{3}]-[\dfrac{4(0)^{3/2}}{3}]$
Therefore, the required area is: $Area=\dfrac{256}{3}$
