Mathematics

Problem

Two functions are defined on the interval

[0,3]

f(x)=\begin{cases}x^{2}, & 0\le x\le 1\\2x-1, & 1< x\le 3\end{cases}\quad\text{and}\quad g(x)=3-x.

Identify the subintervals of

[0,3]

over which separate definite integrals must be set up to compute the exact area of the region enclosed between the graphs of

f

and

g