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Sujay
Find the following integral analytically.
\[\int\limits_{0}^{5} \left| 3x-9 \right| dx\]
\[|3x-9|=\begin{cases}3x-9&\text{if $3x-9\ge0$}\\ -(3x-9)&\text{if $3x-9<0$}\end{cases}=\begin{cases}3x-9&\text{if $x\ge3$}\\ 9-3x&\text{if $x<3$}\end{cases}\] \[\int_0^5|3x-9|\;dx=\int_0^3(9-3x)\;dx+\int_3^5(3x-9)\;dx\]