After the cycle is completed, what is the change in the internal energy of the ideal gas?
No. No need to freak out. The internal energy of the ideal gas depends only on the temperature. After the cycle is completed, the gas returns to its original state – the initial pressure, volume and temperature. That is, after the whole cycle, the temperature does not change and hence, the change in the internal energy ∆E is zero. This is the consequence of internal energy being a state function.