Convergence of Integral

  • Thread starter tbone413
  • Start date
  • #1
7
0

Homework Statement


State whether the problem is convergent or divergent and if its convergent solve the integral. Integral from 0 to inf of (sinx)/(1+cos^2(x))dx


Homework Equations


there isnt really an equation for this, I dont think.


The Attempt at a Solution



Im not really sure how to even start this problem. I know it converges, and I know the answer is pi/4 (the book has the answer) but I am stuck on how to figure out that it A) converges and B) how to solve it.

*I know there are several tests you can use to test for convergence (ratio test, p test, etc.) but im not sure which one applies here.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
It doesn't converge. Find the antiderivative, use u=cos(x). Evaluate it between 0 and L and then let L->infinity. Does it approach a limit?
 

Related Threads on Convergence of Integral

  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
16
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
12
Views
694
  • Last Post
Replies
1
Views
365
  • Last Post
Replies
10
Views
2K
Top