When determining if this integral is convergent or divergent using the f(x) or = g(x) for all x or = a

$$\int\limits_{0}^{\infty} {xdx}/{(1+x^{3})}$$

How do figure out what sign to use? In respect to greater than or equal to or less than or equal to

Question

When determining if this integral is convergent or divergent using the f(x) > or = g(x) for all x > or = a

$$\int\limits_{0}^{\infty} {xdx}/{(1+x^{3})}$$

How do figure out what sign to use? In respect to greater than or equal to or less than or equal to

australopithecus · Answer

I get that you can split the integral to get a separate integral to do the test

$$\int\limits_{0}^{1} xdx/(1+x^{3}) + \int\limits_{1}^{\infty}xdx/(1+x^{3})$$

I know the answer is less than or equal to but I dont understand why

anonymous · Answer

No time to solve this integral, I get http://www.wolframalpha.com/input/?i=integral+xdx%2F%281%2Bx^3%29 And use this tutorial and examples to clarify your doubts http://tutorial.math.lamar.edu/Classes/CalcII/ImproperIntegrals.aspx

australopithecus · Answer

you dont have to solve this integral you just have to show that it is convergent or divergent

australopithecus · Answer

using the rule I outlined you create a new function and compare it

anonymous · Answer

I think I have given the link for tutorial.  Have a look at the examples and try

australopithecus · Answer

Im sorry I dont these problems are related to my question at all
I will show you how my prof did it

australopithecus · Answer

$$x/(1+x^{3}) \le x/(x^{3} + 0)$$

since $$\int\limits_{1}^{\infty} (1/x^{2}) dx$$
is convergent the original integral is convergent

anonymous · Answer

@lgbasallote , can you help here please :)

lgbasallote · Answer

mm sorry i dont know convergent and divergent :C

anonymous · Answer

Same here. Thanks for coming on my request :)

lgbasallote · Answer

athough..why is a calculus question in a physics group :p haha

lgbasallote · Answer

im sure @amistre64 can help..he's good with calculus :)

anonymous · Answer

@amistre64 ,calculus help bro.  Hope you can do it :D

amistre64 · Answer

are we asking why a contiuous sum is greater than a discrete sum?

amistre64 · Answer

imagine it like this; line up a bunch of pennies so they form a contiuous line; count them.

then remove every other penny so that there is a gap between them; then add the up again

the continuous line is greater in value that the discrete line

amistre64 · Answer

if the sum of the greater converges, the lesser has to converge

australopithecus · Answer

still confused but I will try to comprehend what you are saying :L