Aki Posted January 26, 2005 Report Share Posted January 26, 2005 I have this function f(x)=1/x . What would be the intergral from x=1 to x=infinite. Is there a way to calculate that? Because after a while, f(x) would have become so small that it won't matter much. Link to comment Share on other sites More sharing options...
maddog Posted January 26, 2005 Report Share Posted January 26, 2005 I have this function f(x)=1/x . What would be the intergral from x=1 to x=infinite. Is there a way to calculate that? Because after a while, f(x) would have become so small that it won't matter much. Yes, this is possible. Because you are starting at 1 you really can have a definite integralon both sides like so phi(x) = lim x-> 00 integral {1, 00; (1/x) dx} <== I'm using 00 to kinda' look like infinity. I think were to take the limit as x goes to infinity that the integral will diverge. To testthis, use L'Hopital's rule (2nd semester calculus). This should work. ;) Maddog Link to comment Share on other sites More sharing options...
Thelonious Posted January 26, 2005 Report Share Posted January 26, 2005 As maddog said, you can find the definite interval, which uses a limit as the number of subintervals approaches infinity. If you are unfamiliar with this concept, hop on over to Math World for a more in depth analysis, which is too hard to do over this medium. Link to comment Share on other sites More sharing options...
sanctus Posted January 26, 2005 Report Share Posted January 26, 2005 you can already be sure that it will diverge knowing that the sum to infinity over 1/n diverges.... Link to comment Share on other sites More sharing options...
Tim_Lou Posted January 30, 2005 Report Share Posted January 30, 2005 would it be possible so integrate 1/x from 0 to whatever?it is suppose to be undefined... since the "sum" at 0 is undefined. but there is a certain area... so, would it be the area of it? or undefined? Link to comment Share on other sites More sharing options...
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