Ace school

with brainly

  • Get help from millions of students
  • Learn from experts with step-by-step explanations
  • Level-up by helping others

A community for students.

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?

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

I wish I had my calculator on me :( Try comparing it to 1/t.
does it matter whether I compare it to 1/t versus 1/t^2 or 1/t^3, etc?
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.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

It doesn't matter for this case, but for other integrals, you might wanna choose carefully.
I see. thanks. Could I use LCT for this integral as well?

Not the answer you are looking for?

Search for more explanations.

Ask your own question