Single Variable Calculus, Chapter 5, 5.2, Section 5.2, Problem 50

Determine $\displaystyle \int^5_0 f(x) dx$ if
$
f(x) = \left\{
\begin{array}{c}
3 & \text{for} & x < 3\\
x & \text{for} & x \ge 3
\end{array}\right.
$


$
\begin{equation}
\begin{aligned}
\int^5_0 f(x) dx &= \int^3_0 3 dx + \int^5_3 x dx\\
\\
\int^5_0 f(x) dx &= (b-a) + \frac{b^2-a^2}{2}\\
\\
\int^5_0 f(x) dx &= 3(3-0) + \frac{(5)^2-(3)^2}{2}\\
\\
\int^5_0 f(x) dx &= 9+ \frac{25-9}{2}\\
\\
\int^5_0 f(x) dx &= 9 + \frac{16}{2}\\
\\
\int^5_0 f(x) dx &= 9+8\\
\\
\int^5_0 f(x) dx &= 17
\end{aligned}
\end{equation}
$