Let f(x) =
(0) if x< 0
(x) if 0 <= x <= 1
(2 - x) if 1 < x <= 2
(0) if x > 2
and g(x) = [integrate] f(t)dt on [0, x]
i) Find an expression for g(x) similar to the one for f(x).
ii) Where is f differentiable? Where is g differentiable?
I'm pretty much stuck, and don't know how to start this question.
I know first of all that by the fundamental theorem of Calculus, g'(x) = f(x).
But from that, how do I figure out an expression for g(x) from the piecewise function?
Any and all help is appreciated here.