Question

How do you use the comparison test to test for convergence if `1 / (xcosx) dx` from 0 to `pi/2`?

Answer 1

Compare to `1/x^2`.

For `x` close to `0`, we have `x < cosx` so `1/cosx < 1/x` and `1/(xcosx) < 1/x^2`

`int_0^(pi/2) 1/x^2 dx` converges, so does `int_0^(pi/2) 1/(xcosx) dx`