# 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 $$(0,2)$$.

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