From INTEGRATION SIKHO - l l

1 ) integ [ e ^x2 ] = ??????????

Clue : Is it Integrable at all ??????????? : )

how do u knw if a functon is integratable or not????

Only differentiable functions can be integrated

f'(x) = 2x e^x2

LHL ≠RHL

Hence , the function is not differentiable & thus not integrable

2 ) Let f(x) is a quadratic function such that f(0) = 1 & ∫ f(x) dx / (x² (x+1)³ )

is a rational function , find the value of f'(0).

Q2..let f(x)=ax²+bx+c......
f(0)=1,so c=1.
\int bx/(x^{2})(1+x)^{3} is not rational.......
so b=0..
so f(x)=ax²+1,
f'(x)=0

Thanks Rahul
Good solution !!!!!!!!!

Yes Rohit
Rahul is right
LHL ≠RHL at x= 0

since at x=0 LHL <0 & RHL > 0

but we culd integrate it from 1 to n

Ya Rohit That's possible

But in my Qs an indefinite integral is asked for & not a definite one right? :)

I had to start this new thread on INTEGRATION

since I wanted this thread to be free for everyone to add their Qs n we

can have all good Qs on Integration piled up here

NOTE: There is no rule that u need to add Qs only after all the previous ones r answered !!!

But Plz let's restrict the max no. of qs that can remain unanswered at a time to be 5

So , Here we go to become perfect in INTEGRATION for IIT JEE

REQUEST : Do not post Qs out of IIT JEE level

yes dats wht!!but u cant go abt chking every point whether its differntiable or not..??????

@Kartick No. ur Qs I mean it's qs no 4

@Rohit : U know easily that it's differentiable over [-∞,0] & [0, ∞]

but not [-∞,0] U [0,∞]

it is just a function

somebody get mein ques.

@Kaymant : Sir ,

I learnt from a text book published by " Cengage Learning " in an Assertion - Reasoning Qs

Is it wrong ??

Coming to the function e^x2

f'(x) = 2x e^x2

f'(x) < 0 , for x -> 0^- ----- LHL

f'(x) > 0 , for x -> 0⁺ ----- RHL

LHL ≠RHL
So , not differentiable

All integrable functions r differentiable & converse

R they TRUE?????????