To find the area under the graph of a function $f(x)$ over a given interval, you evaluate the definite integral of $f(x)$ across that interval. In this case, the interval is $[e^3, -\frac{1}{e^3}]$.

However, the given interval seems unusual, as it is written in reverse order. If the interval is $[e^3, -\frac{1}{e^3}]$, then the integral will have a negative value due to the reversed limits. Let’s proceed formally:

Definite Integral Formula:

The area under $f(x)$ between $x = a$ and $x = b$ is given by:

$\text{Area} = \int_a^b f(x) \, dx$

If the function $f(x)$ is not specified:

You will need to clarify the function $f(x)$ so we can proceed with its integration.

Reversed interval:

If the limits are reversed, the integral will have a negative sign. This means the calculation should respect:

$\int_{e^3}^{-\frac{1}{e^3}} f(x) \, dx = -\int_{-\frac{1}{e^3}}^{e^3} f(x) \, dx$

Please provide the specific function $f(x)$, or clarify if this is just a conceptual question about the integration bounds.