Question

How do you evaluate the definite integral `int (csc(6theta)-cot(6theta))^2 theta` from `[5,6]`?

Answer 1

The integral diverges.

Explanation:

We are concerned with `csc(x)` and `cot(x)` essentially between `x=25` and `x=30`. Both these functions have asymptotes every `kpi`, where `k` is an integer.

There is guaranteed to be a multiple of `piapprox3.14` in the interval from `25` to `30`, so we know this integral will not converge.

(This answer assumes we're working in radians.)