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Q) The improper integral INT [a,b] f(x) f'(x) dx is

A) necessarily zero
B) possibly 0 but not necessarily
C) necessarily non non existant
D) possibly non existant but not necessarily
E) none of the above

You need to give the function f. Don't expect people to go look stuff up for you.

The question is just as mathQ wrote it, a, b, and f are all arbitrary.

Back to the original: this problem can be simplified using substitution with u=f(x).

I tried that...that would give me the ans ( [f(b)]^2 - [f(a)]^2 )/ 2

is it some printing mistake on the ques paper ?

Okay, sorry, mrb is right, I went back and looked at the problem, at the top of the page it says

Let f be a function such that the graph of f is a semicircle S with end points (a,0) and (b, 0) where a < b

Its the same f which was used for the two previous questions.

Because of the endpoints, f(a) = f(b) = 0

There are two more questions before this question and there is a statement before these questions. all three questions are related to this statement so see this question in view of that statement.