## purplemouse Group Title 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? 2 years ago 2 years ago

1. Rogue Group Title

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

2. purplemouse Group Title

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

3. Rogue Group Title

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. Rogue Group Title

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

5. purplemouse Group Title

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