11Hey,the indefinite integral ∫ex2dx is not integrable!!(I am sure of this)
But the definite integral is.(I positively think so!!)
Hey guys. My friend asked this question to me today and I didn't know how to do it.
Integrate ex2 w.r.t x
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14 Answers
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11Definite integral is integrable but indefinite is not? [7][7][7][7][7]
11Yes!!! Similarly , ∫ (sin x)/x dx --->Not integrable!!
a∫b (sin x)/x dx ----> Integrable!!
11ok. then I'll give my friend a slap. [4]
Also pls evaluate
a∫bex2dx
1it is integrable.using e^x=1+x/1!+....
ans=x+(x^3)/3 +(x^5)/(5*2!)+...........
62it is ..
but if u go by this method.. all continuous functions in the world will become integrable... bcos you can write taylor's expansion series for all continuous functions!!!!
11Bhaiyyah, why can't we integrate using Taylor expansions? [7]
62we can... but it will always give an approximation...
for perfect solution, we need to have the function as a single closed function.
1f(x) = f(a) + f'(a)(x-a) + f''(a) (x-a)^2/2! + ........+
fn(@)* (x-a)^n/n!
where fn is n th derivative and @=a+k(x-a) where 0<k<1
it is called taylor's formula of the function f(x)..
62aragon and akihil it is not in syllabus.. dont read too much into this question... just move on...
1@akhil formula given by u is not complete taylors & mclawrian series go upto infinity ( dont just stop at n)