anonymous 4 years ago Testing for convergence or divergence of an integral: Use the direct comparison test or limit comparison test to test the integral for convergence. integral (0 to 1) of dt/(t-sint) How do I know which test to use, and how should I proceed from there?

1. anonymous

I wish I had my calculator on me :( Try comparing it to 1/t.

2. anonymous

does it matter whether I compare it to 1/t versus 1/t^2 or 1/t^3, etc?

3. anonymous

Yep, this diverges ;) 1/(t - sin t) > 1/t from t:[0,1] $\int\limits_{0}^{1} \frac {dt}{t} = \left[ \ln t \right]_{0}^{1}$ That is divergent. Since 1/t (the smaller function) diverges, then 1/(t- sin t) (the bigger function) must diverge as well.

4. anonymous

It doesn't matter for this case, but for other integrals, you might wanna choose carefully.

5. anonymous

I see. thanks. Could I use LCT for this integral as well?