Evaluate: ∫₋₆³ |x + 3| dx

$|x+3| = -(x+3)$ for $x<-3$ and $x+3$ for $x\ge-3$. $\int_{-6}^{3}|x+3|\,dx = \int_{-6}^{-3}-(x+3)\,dx+\int_{-3}^{3}(x+3)\,dx$ $= -\left[\frac{(x+3)^2}{2}\right]_{-6}^{-3}+\left[\frac{(x+3)^2}{2}\right]_{-3}^{3} = -\left(0-\frac92\right)+\left(18-0\right) = \frac92+18$ Hence the value is $\frac{45}{2}$.