True/false convergence of integral from 1 to infinity

  • #1
217
0
Suppose h(x) is a continuous function for x > 0. If [tex]\int^∞_1{h(x)dx}[/tex] converges then for constant 0 < a < 1, [tex]\int^∞_1{h(\frac{x}{a})dx}[/tex] also converges.

The answer is true. Anyone care to explain why? I would have chosen false, because I was thinking that h(x/a) is larger than h(x) so we wouldn't know if it converges or not.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,836
251
hint: substitution :wink:
 

Related Threads on True/false convergence of integral from 1 to infinity

Replies
8
Views
985
Replies
13
Views
678
Replies
14
Views
799
Replies
5
Views
2K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
1
Views
3K
Replies
10
Views
3K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
1
Views
2K
Top