Final answer:
To evaluate the integral of arccos(cos(x/12x))dx, simplify the expression and evaluate the integral over one period of the cosine function, which is from 0 to 2π. The result is π².
Step-by-step explanation:
To evaluate the integral of arccos(cos(x/12x))dx, we can simplify the expression by noting that arccos(cos(x/12x)) is equal to x over one period of the cosine function. Therefore, we have:
Set the limits of integration from 0 to 2π (one period of the cosine function).
Replace arccos(cos(x/12x)) with x.
Evaluate the integral of x from 0 to 2π.
The result of this integration is π².