From INTEGRATION SIKHO - l l

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

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

errr it doesnt seem to be integatable by byparts atleast...:)

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).

good initiative [1]

LHL≠RHL at x=0....

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,∞]

CAN ANYONE GET IT!!!!!!11

@Kartick what's f here ?????

u din't mention any f in the Qs na?????

@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

Sir plz correct me if I'm wrong
I'm unable to identify the mistake

All integrable functions r differentiable & converse

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