× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
5
a
5
k
5
c
5
B
5
l
5
C
4
s
4
a
4
t
4
i
4
r
4
Home Q & A Board Science-Related Homework Help Mathematics Trending Topics
New Topic  
Fipas Fipas
wrote...
Posts: 55
Rep: 0 0
11 years ago
You have to know whether an improper integral converges before you can evaluate it. How do we do this?

For example,

?
? dx / x^(19/20)
1

It says in the back of my book that this does not converge. How do we find this out?

And what do we determine to tell us that a problem, does indeed, converge?

Thank you
Read 217 times
2 Replies

Related Topics

Replies
wrote...
#1
11 years ago
Evaluate it:


? dx / x^(19/20) [1, ?]

lim... ? dx / x^(19/20) [1, a]
a??

lim... (20x^(1/20)) [1, a]
a??

lim... (20a^(1/20) - 20)
a??

?

integral diverges
wrote...
#2
11 years ago
This type of integral is called a p-integral. It is of the form
int(1/(x^p))dx from x=1 to oo
A p-integral converges when p>1 and diverges if p<1 or p=1.
In our case p=19/20, which means p<1, therefore the integral diverges.
New Topic      
Quick Reply
Explore
Post your homework questions and get free online help from our incredible volunteers
  1260 People Browsing
Start New Topic Take the Tour CoursesNew Study Tools Topics Trending Browse by Textbook
Live Chat
Related Images
  
 261
  
 598
  
 295
Your Opinion
What percentage of nature vs. nurture dictates human intelligence?
Votes: 431
Previous poll results: Which 'study break' activity do you find most distracting?