Answer
$\dfrac{1}{2}$
Work Step by Step
We are given that $y=x$
Here, the area $(A)$ can be expressed as: $A=\int_0^{1} x \ dx$
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 $A=\int_0^{1} x \ dx=[\dfrac{x^2}{2}]_0^1$
or, $=[\dfrac{(1)^2}{2}]-[\dfrac{(0)^2}{2}]$
or, $=\dfrac{1}{2}$
Therefore, the required area is: $Area=\dfrac{1}{2}$
