# convergent/divergent integrals

• Mar 9th 2009, 08:42 PM
buttonbear
convergent/divergent integrals
Suppose f and g are continous functions with f(x)  g(x)  0 for x  a then
(A) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is convergent
(B) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is divergent
(C) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is divergent
(D) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is convergent

i have no idea on this one..(Thinking)
• Mar 9th 2009, 09:21 PM
mollymcf2009
Quote:

Originally Posted by buttonbear
Suppose f and g are continous functions with f(x)  g(x)  0 for x  a then
(A) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is convergent
(B) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is divergent
(C) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is divergent
(D) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is convergent

i have no idea on this one..(Thinking)

Can't read your inequalities in the first part. CAn you tell me what those are?
• Mar 10th 2009, 05:34 AM
Krizalid
I think is \$\displaystyle f(x)\ge g(x)\ge0\$ which can be rewritten backwards as \$\displaystyle 0\le g(x)\le f(x).\$

Following up on this, only these statements hold:

1) If \$\displaystyle f(x)\$ converges, then so does \$\displaystyle g(x).\$

2) If \$\displaystyle g(x)\$ diverges, then so does \$\displaystyle f(x).\$
• Mar 10th 2009, 06:23 AM
buttonbear
thank you so much

i actually just learned this today, and it's on my midterm tomorrow(Wondering)