I know, I need to work hard for improving my English.
I know, I need to work hard to improve my English.
I guess both sentences are correct.
My question is, are "for improving" and "to improve" interchangeable? Please help. I'm really confused.
My question is, are "for improving" and "to improve" interchangeable?
No, they are not interchangeable as you have used them here.
"I know, I need to work hard to improve my English" is the only option that is correct, and the simple present is the best tense for this type of sentence.
For improving your English, there's nothing better than practice.
Typing the same question three times in a row isn't going to make us answer any faster. The opposite, in fact.
if you use for+ing you are laying emphasis on the function that an object may have.
e.g. I need a knife for cutting bread. (it means you need a special knife which serves that purpose or has that function).
If you use the infinitive (TO+verb) the emphasis is laid on the purpose of an action.
I need a knife to cut the bread (it is more focussed on the fact that unless you have a knife, you won't be able to cut the bread)
I hope it helps.