The image shows an integral problem that involves finding the definite integral of the function $(3x - 2)^3$ with respect to $x$ from 0 to 1. The integral is:

$\int_0^1 (3x - 2)^3 \, dx$

Let's solve this step by step.

Step 1: Expand $(3x - 2)^3$

First, expand the cubic expression:

$(3x - 2)^3 = (3x - 2)(3x - 2)(3x - 2)$

Expanding it leads to:

$= 27x^3 - 54x^2 + 36x - 8$

Step 2: Integrate the polynomial

Now, integrate the expanded expression term by term:

[ \int_0^1 (27x^3 - 54x^2 + 36x - 8) , dx \