The area bounded by the line $y=x$, x-axis and ordinates $x=-1$ and $x=2$ is?

To find the area bounded by the line $y = x$, the x-axis, and the vertical lines (ordinates) $x = -1$ and $x = 2$, we shall calculate the definite integral of the function $y = x$ from $-1$ to $2$.

The area $A$ can be calculated as follows:

$A = \int_{-1}^{2} x \, dx$

Calculating the integral, we have:

$A = \left[ \frac{x^2}{2} \right]_{-1}^{2}$

Now, evaluate the integral at the bounds:

$A = \left( \frac{2^2}{2} \right) - \left( \frac{(-1)^2}{2} \right)$ $A = \left( \frac{4}{2} \right) - \left( \frac{1}{2} \right)$ $A = 2 - \frac{1}{2}$ $A = \frac{4}{2} - \frac{1}{2}$ $A = \frac{3}{2}$

Therefore, the area bounded by the line $y = x$, the x-axis, and the ordinates $x = -1$ and $x = 2$ is $\frac{3}{2}$.