Definite Integrals!

Calculus Level 4

If \(y = f(x) \) makes positive intercept of 2 and 0 unit on \(x\) and \(y\) axis respectively and enclose an area of \( \dfrac34\) square units with the \(x\)-axis, find \( \displaystyle \int_0^2 x f'(x) \, dx \).

It is given that \(f(x) \) lies above the \(x\)-axis in the interval \((0,2) \).


This question is a part of the set Calculus.
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