Question

can anybody explain what is the condition for a function to be integrated?

Answer 1

a function must be continuous .... at least one side continuity must exist.

Answer 2

continuity is required for a function to be differentiated ....what about to be integrated?

Answer 3

i'm not expert on analysis
http://en.wikipedia.org/wiki/Riemann_integral#Integrability

Answer 4

I don't think there is a simple set of criteria. Some functions cannot be integrated in terms of simpler functions at all. Some that were thought to be impossible wound up being solved using new approaches.

Answer 5

actually i have been looking for the answer of this question for past 6 months so thought to post it here...

Answer 6

they are varied and it's hard to see whether a function is integrable or not
statistically speaking, most (an infinite number in fact) of functions are non-integrable

for example\[\int\sin(x^2)dx\]looks fairly harmless but is non-integrable by traditional means and cannot be represented in terms of basic functions
(the answer is in terms of something called the Fresnel integral, which I am not familiar with)
http://www.wolframalpha.com/input/?i=integral+sin%28x%5E2%29dx

Answer 7

that is the problem ...i am unable to find the exact conditions for the integration of function

Answer 8

as @experimentX mentioned (at least in pm) was that some of these things are integrable as definite integrals only

as for rules as to when they cannot be integrated (definitely or indefinitely) I do not know of any simple way to tell

Answer 9

looks like relevant topics.
http://www.mymathforum.com/viewtopic.php?f=15&t=29299

Answer 10

thanks guys

Answer 11

np man!!

Answer 12

There are many definitions of integrations. Two of the most used ones are
Riemann integration and Lebesgue integration.
A function f is Riemann integrable on a bounded interval [a,b] if f is bounded
and continuous almost everywhere (ie the set of discontinuities has measure zero in the sense of Lebesgue).
See
http://en.wikipedia.org/wiki/Riemann_integral#Definition

Answer 13

Lebesgue integration is probably beyond the scope of the majority of users on this site.

Answer 14

and one other Question is the condition for indefinite integration not to have closed form?

Answer 15

no it is absolutely fine i have been studying advanced mathematics so can you please elaborate it briefly .. i shall be grateful to you...

Answer 16

^yes, I too would like to hear a bit about it if possible

Answer 17

@eliassaab i request you to explain the boundary conditions in brief ..for integration ..especially the rimeann integrable function

Answer 18

@ghazi what do you mean by boundary conditions for integration?

Answer 19

basically i want to know if i have to integrate a function then according to riemann integrable function how a function is defined to be integrated?

Answer 20

I gave you when a function is Riemann integrable. I should be bounded
and continuous almost everywhere. An integrable function does not have
to have a closed form solution.

Answer 21

For example
\[
f(x) =\frac{1}{1+x^3 +\sin(x^5)}
\]
is integrable on [0,1] but does not have a closed form solution.
integrate 1/(1+x^3 + sin(x^5)) from 0 to 1

Answer 22

http://www.wolframalpha.com/input/?i=integrate+1%2F%281%2Bx^3+%2B+sin%28x^5%29%29+from+0+to+1

Answer 23

okay..thanks a lot sir..i shall go through the link that you've given