Final answer:
To find the area under the curve of f(x) = sin(x)/(1-2cos(x)) from 2π/3 to π, one must compute the definite integral over that interval. The presence of a vertical asymptote complicates the calculation, which may require limits to evaluate.
Step-by-step explanation:
The question asks us to find the area under the curve of the function f(x) = sin(x)/(1-2cos(x)) from x = 2π/3 to x = π. This involves calculating the definite integral of the function over the given interval. To calculate this area, we would typically set up the integral of f(x) from 2π/3 to π and evaluate it.
However, without additional context or details about the integrability and behavior of the function within this interval, an exact answer cannot be provided here. The function given has a vertical asymptote at the values of x where 1 - 2cos(x) = 0, which needs to be addressed in the computation. Therefore, care must be taken to evaluate the integral properly, possibly involving limits if the interval includes points of discontinuity.