Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm tried without sucess to solve this integral: $$\lim_{n\to\infty}\int_{0}^{1}(1+x^2)^{-n}dx$$

I know that the why to solve it ,is by using the Lebesgue dominated convergence theorem.

share|improve this question
    
Hint: look at the function $1/(1+x^2)$. The solution is very straightforward. –  Bruno Joyal Feb 11 '13 at 19:57
    
Yes. Just show that the integrands converge pointwise to ... and that they are dominated by ... –  1015 Feb 11 '13 at 20:00
    
When asking questions on this site it is customary to include your thoughts about the problem as well as what you have tried to do to solve it. –  Antonio Vargas Feb 11 '13 at 20:25
    
OK, I see that the integrands converge to pi/4 (without the limit) but what about n ? –  user61801 Feb 11 '13 at 20:53
2  
First calculate $$ \lim_{n \to \infty} (1+x^2)^{-n}, $$ then use the dominated convergence theorem to say that $$ \lim_{n \to \infty} \int_0^1 (1+x^2)^{-n} \,dx = \int_0^1 \left(\,\lim_{n \to \infty} (1+x^2)^{-n}\right) \,dx. $$ Which part is giving you trouble? –  Antonio Vargas Feb 11 '13 at 22:09

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.