Consider the provided figure. Suppose Δ U_1 and Δ U_2 denote the...

Internal energy is a state function, which means that the change in internal energy of a thermodynamic system depends only on its initial and final states, and is independent of the path taken between them.

From the given $p-V$ diagram, it is clear that both processes $A$ and $B$ begin at the same initial state and terminate at the same final state.

Since the initial and final states are identical for both processes, the change in internal energy must be the same for both paths.

Therefore, $\Delta U_1 = \Delta U_2$.